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This paper introduces SideSeeing, a novel initiative that provides tools and datasets for assessing the built environment. We present a framework for street-level data acquisition, loading, and analysis. Using the framework, we collected a novel dataset that integrates synchronized video footaged captured from chest-mounted mobile devices with sensor data (accelerometer, gyroscope, magnetometer, and GPS). Each data sample represents a path traversed by a user filming sidewalks near hospitals in Brazil and the USA. The dataset encompasses three hours of content covering 12 kilometers around nine hospitals, and includes 325,000 video frames with corresponding sensor data. Additionally, we present a novel 68-element taxonomy specifically created for sidewalk scene identification. SideSeeing is a step towards a suite of tools that urban experts can use to perform in-depth sidewalk accessibility evaluations. SideSeeing data and tools are publicly available at https://sites.usp.br/sideseeing/., Comment: 11 pages, 7 figures

The scalar sector of the Myers and Pospelov model is considered. This theory introduces a dimension 5 operator with a preferred four-vector which breaks Lorentz symmetry. We investigate various applications using the TFD formalism, a topological field theory that allows the study of thermal and size effects on an equal footing. In this context, Lorentz-violating corrections to the Casimir effect and Stefan-Boltzmann law have been calculated., Comment: 17 pages

We present the results of a size and structural analysis of 1395 galaxies at $0.5 \leq z \lesssim 8$ with stellar masses $\log \left(M_* / M_{\odot}\right)$ $>$ 9.5 within the JWST Public CEERS field that overlaps with the HST CANDELS EGS observations. We use GALFIT to fit single S\'ersic models to the rest-frame optical profile of our galaxies, which is a mass-selected sample complete to our redshift and mass limit. Our primary result is that at fixed rest-frame wavelength and stellar mass, galaxies get progressively smaller, evolving as $\sim (1+z)^{-0.71\pm0.19}$ up to $z \sim 8$. We discover that the vast majority of massive galaxies at high redshifts have low S\'ersic indices, thus do not contain steep, concentrated light profiles. Additionally, we explore the evolution of the size-stellar mass relationship, finding a correlation such that more massive systems are larger up to $z \sim 3$. This relationship breaks down at $z > 3$, where we find that galaxies are of similar sizes, regardless of their star formation rates and S\'ersic index, varying little with mass. We show that galaxies are more compact at redder wavelengths, independent of sSFR or stellar mass up to $z \sim 3$. We demonstrate the size evolution of galaxies continues up to $z \sim 8$, showing that the process or causes for this evolution is active at early times. We discuss these results in terms of ideas behind galaxy formation and evolution at early epochs, such as their importance in tracing processes driving size evolution, including minor mergers and AGN activity., Comment: Submitted to MNRAS

In this paper, the aether field, which leads to the violation of Lorentz symmetries, coupled with the electromagnetic field is considered. In order to study thermal and size effects in this theory, the Thermo Field Dynamics (TFD) formalism is used. TFD is a real-time quantum field theory that has an interesting topological structure. Here three different topologies are taken, then three different phenomena are calculated. These effects are investigated considering that the aether field can point in different directions. The results obtained are compared with the usual results of the Lorentz invariant electromagnetic field., Comment: 15 pages, accepted for publication in EPJP

In this work, we study and evaluate the impact of a periodic spin-lattice coupling in an Ising-like system on a 2D triangular lattice. Our proposed simple Hamiltonian considers this additional interaction as an effect of preferential phonon propagation direction augmented by the symmetry ofthe underline lattice. The simplified analytical description of this new model brought us consistent information about its ground state and thermal behavior, and allowed us to highlight a singularity where the model behaves as several decoupled one-dimensional Ising systems. A thorough analysis was obtained via entropic simulations based in the Wang-Landau method that estimates the density of states g(E) to explore the phase diagram and other thermodynamic properties of interest. Also, we used the finite size scaling technique to characterize the critical exponents and the nature of the phase transitions that, despite the strong influence of the spin-lattice coupling, turned out to be within the same universality class as the original 2D Ising model.

We present an early analysis on the search for high redshift galaxies using the deepest public JWST imaging to date, the NGDEEP field. This data consists of 6-band NIRCam imaging on the Hubble Ultra Deep Field-Par2, covering a total area of 6.3 arcmin$^{2}$. Based on our initial reduction of the first half of this survey, we reach 5$\sigma$ depths up to mag = 29.5--29.9 between $1-5$ um. Such depths present an unprecedented opportunity to begin exploring the early Universe with JWST. As such, we find high redshift galaxies in this field by examining the spectral energy distribution of these systems and present 18 new $z > 8$ systems identified using two different photometric redshift codes: LePhare and EAZY, combined with other significance criteria. The highest redshift object in our sample is at $z=15.57^{+0.39}_{-0.38}$, which has a blue beta slope of $\beta=-3.25^{+0.41}_{-0.46}$ and a very low inferred stellar mass of $M_{*} = 10^{7.39}$ M_0,. We also discover a series of faint, low-mass dwarf galaxies with $M_{*} < 10^{8.5}$ M_0 at $z \sim 9$ that have blue colors and UV slopes. The structure of these galaxies is such that they all have very flat surface brightness profiles and small sizes $< 1 \ \mathrm{kpc}$. We also compare our results to theory, finding no significant disagreement with some CDM based models.The discovery of these objects, most of which are low luminosity and inferred stellar mass, demonstrates the power of probing continuously deeper into the Universe, pointing the way to deeper, or similar depth but wider area, surveys and demonstrate the critical need for JWST deep fields to explore this aspect of the early Universe., Comment: ApJL submitted. Added acknowledgements and slight change in title. Mosaics of our NGDEEP reductions are available here: tinyurl.com/yckcfnxu

Boltzmann's microcanonical entropy is the link between statistical physics and thermodynamics, forasmuch as the behavior of any thermodynamic quantity is directly related to the number of microscopic configurations. Accordingly, in this work, we investigate the behavior of the logarithm of the density of states of the three-state Potts model with an external field applied to one of the states using joint entropic simulations based on the Wang-Landau algorithm. Our analysis reveals that the microcanonical entropy curve is detachable, and each resulting path is related to the formation of clusters. Such a description is consistent with the energy-entropy argument related to the inception of a phase transition. When the external field is reversed and strong, the observed phase transition is from an ordered configuration to cluster formations. The behavior of the microcanonical inverse temperature indicates both first and second-order phase transitions occurring at different temperatures for high values of the external field.

The various Euclid imaging surveys will become a reference for studies of galaxy morphology by delivering imaging over an unprecedented area of 15 000 square degrees with high spatial resolution. In order to understand the capabilities of measuring morphologies from Euclid-detected galaxies and to help implement measurements in the pipeline, we have conducted the Euclid Morphology Challenge, which we present in two papers. While the companion paper by Merlin et al. focuses on the analysis of photometry, this paper assesses the accuracy of the parametric galaxy morphology measurements in imaging predicted from within the Euclid Wide Survey. We evaluate the performance of five state-of-the-art surface-brightness-fitting codes DeepLeGATo, Galapagos-2, Morfometryka, Profit and SourceXtractor++ on a sample of about 1.5 million simulated galaxies resembling reduced observations with the Euclid VIS and NIR instruments. The simulations include analytic S\'ersic profiles with one and two components, as well as more realistic galaxies generated with neural networks. We find that, despite some code-specific differences, all methods tend to achieve reliable structural measurements (10% scatter on ideal S\'ersic simulations) down to an apparent magnitude of about 23 in one component and 21 in two components, which correspond to a signal-to-noise ratio of approximately 1 and 5 respectively. We also show that when tested on non-analytic profiles, the results are typically degraded by a factor of 3, driven by systematics. We conclude that the Euclid official Data Releases will deliver robust structural parameters for at least 400 million galaxies in the Euclid Wide Survey by the end of the mission. We find that a key factor for explaining the different behaviour of the codes at the faint end is the set of adopted priors for the various structural parameters., Comment: Accepted by A&A. 30 pages, 23+6 figures, Euclid pre-launch key paper. Companion paper: Euclid Collaboration XXV: Merlin et al. 2022 Minor corrections after journal review

The ESA Euclid mission will provide high-quality imaging for about 1.5 billion galaxies. A software pipeline to automatically process and analyse such a huge amount of data in real time is being developed by the Science Ground Segment of the Euclid Consortium; this pipeline will include a model-fitting algorithm, which will provide photometric and morphological estimates of paramount importance for the core science goals of the mission and for legacy science. The Euclid Morphology Challenge is a comparative investigation of the performance of five model-fitting software packages on simulated Euclid data, aimed at providing the baseline to identify the best suited algorithm to be implemented in the pipeline. In this paper we describe the simulated data set, and we discuss the photometry results. A companion paper (Euclid Collaboration: Bretonni\`ere et al. 2022) is focused on the structural and morphological estimates. We created mock Euclid images simulating five fields of view of 0.48 deg2 each in the $I_E$ band of the VIS instrument, each with three realisations of galaxy profiles (single and double S\'ersic, and 'realistic' profiles obtained with a neural network); for one of the fields in the double S\'ersic realisation, we also simulated images for the three near-infrared $Y_E$, $J_E$ and $H_E$ bands of the NISP-P instrument, and five Rubin/LSST optical complementary bands ($u$, $g$, $r$, $i$, and $z$). To analyse the results we created diagnostic plots and defined ad-hoc metrics. Five model-fitting software packages (DeepLeGATo, Galapagos-2, Morfometryka, ProFit, and SourceXtractor++) were compared, all typically providing good results. (cut), Comment: 29 pages, 33 figures. Euclid pre-launch key paper. Companion paper: Bretonniere et al. 2022

We compare the two largest galaxy morphology catalogues, which separate early and late type galaxies at intermediate redshift. The two catalogues were built by applying supervised deep learning (convolutional neural networks, CNNs) to the Dark Energy Survey data down to a magnitude limit of $\sim$21 mag. The methodologies used for the construction of the catalogues include differences such as the cutout sizes, the labels used for training, and the input to the CNN - monochromatic images versus $gri$-band normalized images. In addition, one catalogue is trained using bright galaxies observed with DES ($i<18$), while the other is trained with bright galaxies ($r<17.5$) and `emulated' galaxies up to $r$-band magnitude $22.5$. Despite the different approaches, the agreement between the two catalogues is excellent up to $i<19$, demonstrating that CNN predictions are reliable for samples at least one magnitude fainter than the training sample limit. It also shows that morphological classifications based on monochromatic images are comparable to those based on $gri$-band images, at least in the bright regime. At fainter magnitudes, $i>19$, the overall agreement is good ($\sim$95\%), but is mostly driven by the large spiral fraction in the two catalogues. In contrast, the agreement within the elliptical population is not as good, especially at faint magnitudes. By studying the mismatched cases we are able to identify lenticular galaxies (at least up to $i<19$), which are difficult to distinguish using standard classification approaches. The synergy of both catalogues provides an unique opportunity to select a population of unusual galaxies., Comment: 17 pages, 14 figures (1 appendix for galaxy examples including 3 figures)

We present a reduction and analysis of the \textit{James Webb Space Telescope} (JWST) SMACS~0723 field using new post-launch calibrations to conduct a search for ultra-high-redshift galaxies ($z > 9$) present within the Epoch of Reionisation. We conduct this search by modelling photometric redshifts in several ways for all sources and by applying conservative magnitude cuts ($m_{\rm F200W} < 28$) to identify strong Lyman breaks greater than 1 magnitude. We find four $z > 9$ candidate galaxies which have not previously been identified, with one object at $z = 11.5$, and another which is possibly a close pair of galaxies. We measure redshifts for candidate galaxies from other studies and find the recovery rate to be only 23 per cent, with many being assigned lower redshift, dusty solutions in our work. Most of our $z > 9$ sample show evidence for Balmer-breaks, or extreme emission lines from H$\beta$ and [OIII], demonstrating that the stellar populations could be advanced in age or very young depending on the cause of the F444W excess. We discuss the resolved structures of these early galaxies and find that the S\'{e}rsic indices reveal a mixture of light concentration levels, but that the sizes of all our systems are exceptionally small ($< 0.5$~kpc). These systems have stellar masses M$_{*} \sim 10^{9.0}$ M$_{\odot}$, with our $z \sim 11.5$ candidate a dwarf galaxy with a stellar mass M$_{*} \sim 10^{7.8}$ -- $10^{8.2}$ M$_{\odot}$. These candidate ultra high-redshift galaxies are excellent targets for future NIRSpec observations aimed to better understand their physical nature., Comment: Updated to accepted mnras manuscript, 12 pages, 8 figures, 6 tables, added section 3.3 and Table 5

It has been recently proposed a modification of the Skyrme model which admits an exact self-dual sector by the introduction of six scalar fields assembled in a symmetric, positive and invertible 3x3 matrix h. In this paper we study soft manners of breaking the self-duality of that model. The crucial observation is that the self-duality equations impose distinct conditions on the three eigenvalues of h, and on the three fields lying in the orthogonal matrix that diagonalizes h. We keep the self-duality equations for the latter, and break those equations associated to the eigenvalues. We perform the breaking by the addition of kinetic and potential terms for the h-fields, and construct numerical solutions using the gradient flow method to minimize the static energy. It is also shown that the addition of just a potential term proportional to the determinant of h, leads to a model with an exact self-dual sector, and with self-duality equations differing from the original ones by just an additional coupling constant., Comment: 29 pages, 3 figures

One of the most active research fields in single-pixel imaging is the influence of the sampling basis and its order in the quality of the reconstructed images. This paper presents two new orders, ascending scale (AS) and ascending inertia (AI), of the Hadamard basis and test their performance, using simulation and experimental methods, for low sampling ratios (0.5 to 0.01). These orders were compared with two state-of-the-art orders, cake-cutting (CC) and total gradient (TG), using TVAL3 as the reconstruction algorithm and three noise levels. These newly proposed orders have better reconstructed image quality on the simulation data set (110 images) and achieved structure similarity index values higher than CC order. The experimental data set (2 images) showed that the AS and AI orders performed better with a sampling ratio of 0.5, while for lower sampling ratio the performance of AS, AI and CC was similar. The TG order performed worst in the majority of the cases. Finally, the simulation results present clear evidence that peak signal-to-noise ratio (PSNR) is not a reliable image quality assessment (IQA) metric to assess image reconstruction quality in the context of single pixel imaging.

The Thermofield Dynamics (TFD) formalism is considered. In this context, a Lorentz-breaking scalar field theory is introduced. In contrast to the Matsubara formalism, the best-known approach to introducing the temperature effect, TFD is a real-time formalism and is a topological field theory. While in Matsubara the temperature effects are introduced as a consequence of a compactification of the field in a finite interval on the time axis, in the TFD this effect emerges through a condensed state related to the Bogoliubov transformation. An advantage of the TFD formalism is that different topologies, which lead to different effects, can be chosen. Here, three different topologies are considered. Then the Stefan-Boltzmann law and Casimir effect at zero and non-zero temperature are calculated. This is a unique feature of TFD, which allows us to treat different phenomena in the same way., Comment: 16 pages, accepted for publication in PLB

Here we present a new perspective to the breakdown of ferromagnetic order in two-dimensional spin-lattice models employing the rotation of the underlying lattice. Using an Ising spin system on a square lattice as a prototype, we demonstrate that an additional low-symmetry interaction may lead to the absence of the truly long-range order and forms aperiodic structure, such as magnetic stripes. Employing annealing and entropic Monte Carlo simulations, we show that our model allows tuning between different phases, magnetically ordered as well as more exotic nonmagnetic phases such as Ising-nematic by changing only one control parameter, which is responsible for the arising of magnetic frustration. In addition, our methodology of considering the coupling between the magnetic structure and the host material can be extended to the study of any type of spin-exchange model in two dimensions and has many potential interesting ramifications and applications.

Self-duality is a very important concept in the study and applications of topological solitons in many areas of Physics. The rich mathematical structures underlying it lead, in many cases, to the development of exact and non-perturbative methods. We present a generalization of the Yang-Mills-Higgs system by the introduction of scalar fields assembled in a symmetric and invertible matrix h of the same dimension as the gauge group. The coupling of such new fields to the gauge and Higgs fields is made by replacing the Killing form, in the contraction of the group indices, by the matrix h in the kinetic term for the gauge fields, and by its inverse in the Higgs field kinetic term. The theory is conformally invariant in the three dimensional space R^3. An important aspect of the model is that for practically all configurations of the gauge and Higgs fields the new scalar fields adjust themselves to solve the modified self-duality equations. We construct solutions using a spherically symmetric ans\"atz and show that the 't Hooft-Polyakov monopole becomes a self-dual solution of such modified Yang-Mills-Higgs system. We use an ans\"atz based on the conformal symmetry to construct vacuum solutions presenting non-trivial toroidal magnetic fields., Comment: 20 pages, 9 figures, version to appear in Physical Review D

The low energy regime of Quantum Chromodynamics (QCD) presents enormous challenges due to its large coupling. Effective field theories, like the Skyrme model, are useful approaches to study properties of strong interaction at hadronic scales. We propose a Skyrme-type model with a self-dual sector and that treats the density of the baryonic charge as a self-interacting fluid. The dynamics reduces to Coleman's false vacuum problem for a scalar field that is a fractional power of that density. The main result is that such a Skyrme-type model is the first one to reproduce, with good accuracy, the experimental values of radii and binding energies for a very wide range of the mass number. The robust and simple properties of the model lead to many possible generalizations with implications not only in nuclear physics but also in other areas of Physics., Comment: Version published in Journal Phys. G: Nucl. Part. Phys. 49 115102 (2022)

A fundamental feature of galaxies is their structure, yet we are just now understanding the evolution of structural properties in quantitative ways. As such, we explore the quantitative non-parametric structural evolution of 16,778 galaxies up to $z\sim3$ in all five CANDELS fields, the largest collection of high resolution images of distant galaxies to date. Our goal is to investigate how the structure, as opposed to size, surface brightness, or mass, changes with time. In particular, we investigate how the concentration and asymmetry of light evolve in the rest-frame optical. To interpret our galaxy structure measurements, we also run and analyse 300 simulation realisations from IllustrisTNG to determine the timescale of mergers for the CAS system. We measure that from $z=0-3$, the median asymmetry merger timescale is $0.56^{+0.23}_{-0.18}$Gyr, and find it does not vary with redshift. Using this data, we find that galaxies become progressively asymmetric at a given mass at higher redshifts and we derive merger rates which scale as $\sim(1+z)^{1.87\pm0.04}$Gyr$^{-1}$, which agrees well with recent machine learning and galaxy pair approaches, removing previous inconsistencies. We also show that far-infrared selected galaxies that are invisible to \textit{HST} have a negligible effect on our measurements. We also find that galaxies are more concentrated at higher redshifts. We interpret this as a sign of how their formation occurs from a smaller initial galaxy that later grows into a larger one through mergers, consistent with the size growth of galaxies from `inside-out', suggesting that the centres are the oldest parts of most galaxies., Comment: Submitted to ApJ. 26 pages, 19 figures

At high redshift, due to both observational limitations and the variety of galaxy morphologies in the early universe, measuring galaxy structure can be challenging. Non-parametric measurements such as the CAS system have thus become an important tool due to both their model-independent nature and their utility as a straightforward computational process. Recently, convolutional neural networks (CNNs) have been shown to be adept at image analysis, and are beginning to supersede traditional measurements of visual morphology and model-based structural parameters. In this work, we take a further step by extending CNNs to measure well known non-parametric structural quantities: concentration ($C$) and asymmetry ($A$). We train CNNs to predict $C$ and $A$ from individual images of $\sim 150,000$ galaxies at $0 < z < 7$ in the CANDELS fields, using Bayesian hyperparameter optimisation to select suitable network architectures. Our resulting networks accurately reproduce measurements compared with standard algorithms. Furthermore, using simulated images, we show that our networks are more stable than the standard algorithms at low signal-to-noise. While both approaches suffer from similar systematic biases with redshift, these remain small out to $z \sim 7$. Once trained, measurements with our networks are $> 10^3$ times faster than previous methods. Our approach is thus able to reproduce standard measures of non-parametric morphologies and shows the potential of employing neural networks to provide superior results in substantially less time. This will be vital for making best use of the large and complex datasets provided by upcoming galaxy surveys, such as Euclid and Rubin-LSST., Comment: 18 pages, 13 figures, accepted for publication in ApJ

We investigate the critical behavior of the two-dimensional spin-$1$ Baxter-Wu model in a crystal field using entropic sampling simulations with the joint density of states. We obtain the temperature-crystal field phase diagram, which includes a tetracritical line ending at a pentacritical point. A finite-size scaling analysis of the maximum of the specific heat, while changing the crystal field anisotropy, is used to obtain a precise location of the pentacritical point. Our results give the critical temperature and crystal field as $T_{pc}=0.98030(10)$ and $D_{pc}=1.68288(62)$. We also detect that at the first-order region of the phase diagram, the specific heat exhibits a double peak structure as in the Schottky-like anomaly, which is associated with an order-disorder transition., Comment: 7 pages. 7 figures

In this work, we investigate the Bell-Lavis model using entropic simulations for several values of the energy parameters. The $T\times\mu$ phase diagram and the ground state configurations are analyzed thoroughly. Besides, we examine the particle density and specific heat behavior for different values of the chemical potential $\mu$ as functions of temperature. We also obtain configurations that maximize the canonical probability for several values of chemical potential and temperature, enabling the identification of the low density ($LDL$) and high-density liquid ($HDL$) phases, among others, in the critical regions. We found a second-order phase transition from the $LDL-HDL_0$ to $LDL-HDL$ coexistence in the range of $0<\mu<1.05503$. In the $1.05503<\mu<1.48024$ range, the transition between the $LDL-HDL_0$ and $LDL-HDL_0-empty$ coexistence presents discontinuous and continuous transitions characteristics. Finally, for $1.48024<\mu<1.5$, the phase transition between $LDL$ and $empty$ phases is of first-order., Comment: 10 pages, 12 figures

In this paper we propose a bimodal gamma distribution using a quadratic transformation based on the alpha-skew-normal model. We discuss several properties of this distribution such as mean, variance, moments, hazard rate and entropy measures. Further, we propose a new regression model with censored data based on the bimodal gamma distribution. This regression model can be very useful to the analysis of real data and could give more realistic fits than other special regression models. Monte Carlo simulations were performed to check the bias in the maximum likelihood estimation. The proposed models are applied to two real data sets found in literature., Comment: 26 pages, 13 figures. Accepted for publication in Statistics: A Journal of Theoretical and Applied Statistics

The crystal growth and the structural, transport and magnetic properties of the magnetically frustrated YbMn$_2$Sb$_2$ single crystals are reported. The crystals show a trigonal symmetry (space group $P\bar{3}m1$), where corrugated honeycomb layers of MnSb are separated by Yb atoms. No structural phase transition was observed down to 22~K. The resistivity measurements show a predominantly insulating behavior. The combined resistivity, dc susceptibility and heat capacity measurements confirm successive transitions at 230~K, 116~K and 27~K, being the transition at $T_N$=116~K due to the Mn$^{+2}$ lattice antiferromagnetic ordering. Muon spin rotation experiments ($\mu$SR) reveal a more complicated scenario, with temperature dependence of the magnetic volume fraction reflecting short range and long range magnetic order, and a strongly disordered magnetic ground state. The role of spin-lattice coupling and its relationship with exchange interactions between Mn moments are discussed as possible cause of the complex magnetic behavior observed.

We study a recently proposed modification of the Skyrme model that possesses an exact self-dual sector leading to an infinity of exact Skyrmion solutions with arbitrary topological (baryon) charge. The self-dual sector is made possible by the introduction, in addition to the usual three SU(2) Skyrme fields, of six scalar fields assembled in a symmetric and invertible three dimensional matrix h. The action presents quadratic and quartic terms in derivatives of the Skyrme fields, but instead of the group indices being contracted by the SU(2) Killing form, they are contracted with the h-matrix in the quadratic term, and by its inverse on the quartic term. Due to these extra fields the static version of the model, as well as its self-duality equations, are conformally invariant on the three dimensional space R^3. We show that the static and self-dual sectors of such a theory are equivalent, and so the only non-self-dual solution must be time dependent. We also show that for any configuration of the Skyrme SU(2) fields, the h-fields adjust themselves to satisfy the self-duality equations, and so the theory has plenty of non-trivial topological solutions. We present explicit exact solutions using a holomorphic rational ansatz, as well as a toroidal ansatz based on the conformal symmetry. We point to possible extensions of the model that break the conformal symmetry as well as the self-dual sector, and that can perhaps lead to interesting physical applications., Comment: 25 pages, no figures, version published in JHEP 09 (2020) 031

The statement that any phase transition is related to the appearance or disappearance of long-range spatial correlations precludes a finite transition temperature in one-dimensional (1D) systems. In this paper we demonstrate that the 1D Ising model with short-range exchange interactions exhibits a second-order phase transition at a finite temperature relying on the proper choice of the order parameter. To accomplish this, we combined analytical calculations and high-precision entropic sampling simulations and chose a slightly different order parameter, namely the module of the magnetization. Notably, we detected a phase transition with a corresponding critical temperature around 15 K, which is in excellent agreement with experimental results. Our study indicates that an inappropriate choice of the order parameter may mask phase transitions in one-dimensional systems.