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We argue that the elastic backbone (EB) (union of shortest paths) on a cylindrical system, studied by Sampaio Filho et al [2018 Phys. Rev. Lett. 120 175701], is in fact the backbone of two-dimensional directed percolation (DP). We simulate the EB on the same system as considered by these authors, and also study the DP backbone directly using an algorithm that allows backbones to be generated in a completely periodic manner. We find that both the EB in the bulk and the DP backbone have a fractal dimension of d b = d B,DP = 1.681 02(15) at the identical critical point p c,DP ≈ 0.705 485 22. We also measure the fractal dimension at the edge of the EB system and for the full DP clusters, and find d e = d DP = 1.840 54(4). We argue that those two fractal dimensions follow from the DP exponents as d B,DP = 2 âˆ' 2 β / ν ∥ = 1.681 072(12) and d DP = 2 âˆ' β / ν ∥ = 1.840 536(6). Our fractal dimensions differ from the value 1.750(3) found by Sampaio Filho et al. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a theoretical approach to calculate site percolation thresholds on two-dimensional lattices is proposed. The method, based on exact counting of configurations on finite cells, arises as a generalization of the analytical approximation introduced by Rosowsky (2000). The resulting methodology was applied to calculate the percolation thresholds corresponding to four systems: monomers on honeycomb lattices (p c = 0. 71278), dimers on square lattices (p c = 0. 5713), dimers on honeycomb lattices (p c = 0. 6653) and dimers on triangular lattices (p c = 0. 4783). The obtained results are in good agreement with previous values calculated by very accurate simulations: 0.69704, 0.5649, 0.6902 and 0.4872. The technique can be easily extended to deal with three-dimensional lattices. Highlights • The percolation problem of monomers and dimers on 2D lattices is studied. • A theoretical approach based on counting configurations on finite cells is applied. • Percolation thresholds are reported. • The obtained results are in good agreement with previous calculations in the literature. [ABSTRACT FROM AUTHOR]

The phase behaviour of aligned rigid rods of length k ( k -mers) adsorbed on two-dimensional square lattices has been studied by Monte Carlo (MC) simulations and histogram reweighting technique. The k -mers, containing k identical units (each one occupying a lattice site) were deposited along one of the directions of the lattice. In addition, attractive lateral interactions were considered. The methodology was applied, particularly, to the study of the critical point of the condensation transition occurring in the system. The process was monitored by following the fourth order Binder cumulant as a function of temperature for different lattice sizes. The results, obtained for k ranging from 2 to 7, show that: (i) the transition coverage exhibits a decreasing behaviour when it is plotted as a function of the k -mer size and (ii) the transition temperature, T c , exhibits a power law dependence on k , T c ∼ k 0 , 4 , shifting to higher values as k increases. Comparisons with an analytical model based on a generalization of the Bragg–Williams approximation (BWA) were performed in order to support the simulation technique. A significant qualitative agreement was obtained between BWA and MC results. [ABSTRACT FROM AUTHOR]

A simple method to estimate percolation thresholds p c in lattice models is presented. The technique is based on the calculation of the probabilities R L X (p) for finding a percolating cluster of type X [ X could be horizontal (H), vertical (V), average (A), intersection (I), or union (U)] on a finite lattice of side length L at concentration p of occupied sites. The functions R L X (p) are obtained by numerical simulations. Then, (1) effective percolation thresholds p c X , r (L) are estimated from the condition R L X (p) = r (where r is a parameter ranging between 0 and 1); and (2) the percolation threshold in the thermodynamic limit is determined by extrapolating the effective percolation thresholds to infinite L. The methodology presented herein contains and extends the classical scheme developed by Yonezawa, Sakamoto and Hori, offering a more complete and versatile theoretical/simulation framework to calculate percolation thresholds. The approach is validated by successfully comparing with well-known results obtained for the problem of random site percolation on square lattices. Taking advantage of the behavior of the curves of p c X , r (L) for different values of the parameter r , more general scaling relations are proposed for the effective percolation thresholds. Finally, the technique is applied to model experimental data of clogging transitions in a two-dimensional silo with a vibrated base. • A new procedure to calculate percolation thresholds in lattice systems is presented. • Multiple effective thresholds are obtained from the percolation probability functions. • The method is applied to the problem of random site percolation on square lattices. • The obtained results are in good agreement with previous calculations in literature. • The clogging transition in a 2D silo is discussed in terms of percolation theory. [ABSTRACT FROM AUTHOR]

Thermodynamics of straight k -mers gas on the square lattice is addressed from its relation to state exclusion statistics through a new analytical approximation along with a detailed MC analysis. Multiple state exclusion arising as consequence of the spatial correlation between particle states is described through exclusion spectrum functions and related to the thermodynamic potentials. An effective lattice analytical approximation is introduced through configurational mapping and applied to dimers (k = 2) and trimers (k = 3). Simple closed analytical forms for the coverage dependence of multiple state exclusion probabilities and chemical potential are obtained. Remarkable agreement with fast relaxation MC simulations carried out in this work is already found for the lowest degree of approximation. • A new approach to model multisite occupancy adsorption is presented. • The formalism is based on statistics of multiple excluded states. • The theory is applied to a lattice-gas model of straight rigid k-mers on square lattices. • An analytical expression for the adsorption isotherm is obtained for dimers and trimers. • Theoretical results are compared with Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

It is known that the Maximum relative Entropy (MrE) method can be used to both update and approximate probability distributions functions in statistical inference problems. In this manuscript, we apply the MrE method to infer magnetic properties of ferromagnetic materials. In addition to comparing our approach to more traditional methodologies based upon the Ising model and Mean Field Theory, we also test the effectiveness of the MrE method on conventionally unexplored ferromagnetic materials with defects . [ABSTRACT FROM AUTHOR]

Random sequential adsorption of straight rigid rods of length k ( k -mers) on a simple cubic lattice has been studied by numerical simulations and finite-size scaling analysis. The k -mers were irreversibly and isotropically deposited into the lattice. The calculations were performed by using a new theoretical scheme, whose accuracy was verified by comparison with rigorous analytical data. The results, obtained for k ranging from 2 to 64, revealed that (i) the jamming coverage for dimers ( k = 2 ) is θ j = 0.918388 ( 16 ) . Our result corrects the previously reported value of θ j = 0.799 ( 2 ) (Tarasevich and Cherkasova, 2007); (ii) θ j exhibits a decreasing function when it is plotted in terms of the k -mer size, being θ j ( ∞ ) = 0.4045 ( 19 ) the value of the limit coverage for large k ’s; and (iii) the ratio between percolation threshold and jamming coverage shows a non-universal behavior, monotonically decreasing to zero with increasing k . [ABSTRACT FROM AUTHOR]

In this paper, the adsorption of interacting binary mixtures on square lattices has been studied. By using Monte Carlo simulation and finite-size scaling analysis, the connection between the surface ordered phases and the percolating properties of the adsorbed phase has been investigated. A rich phase diagram separating a percolating from a non-percolating region has been determined. The main features of the phase diagram have been discussed in terms of simple considerations related to the interactions present in the problem. [ABSTRACT FROM AUTHOR]

The site-bond percolation problem in two-dimensional (3,12 2) lattices has been studied by means of numerical simulation and analytical calculations. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as S ∩ B and S ∪ B) were considered. In S ∩ B (S ∪ B), two points are connected if a sequence of occupied sites AND (OR) bonds joins them. The analytical method is based on the approximation introduced by Tsallis (2004), which allows to calculate the S ∩ B and S ∪ B percolation functions from the percolation functions corresponding to pure site and pure bond percolation problems. Theoretical and numerical data (supplemented by analysis using finite-size scaling theory) were used to determine, for the first time, the complete phase diagram of the system (phase boundary between the percolating and nonpercolating regions). Comparisons between results obtained using the Tsallis's scheme and simulation data were performed in order to test the reaches and limitations of the approach developed here. [ABSTRACT FROM AUTHOR]

Examines the stiffness exponents in the glass phase for lattice spin glasses. Methods used to determine stiffness exponents; Description of the reduction rules for low-connected spins; Analysis of the ground state energy of the reduced graph with external optimization heuristic.

Examines the surface structures of the tellurium/nickel (111) system by using reflection high-energy electron diffraction combined with X-ray and ultraviolet photoelectron spectroscopies. Characterization of temperature phases; Adsorption of tellurium on nickel substrate; Mathematical formulas for tellurium/nickel surface characterization.

The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by the breaking of reparametrization invariance of a Parisi type solution. Twisted boundary conditions are thus imposed at two opposite ends of the system in order to study the size dependence of the twist free energy. A loop-expansion is performed to first order around a twisted background. It is found, as expected but it is non trivial, that the theory does renormalize around such backgrounds, as well as for the bulk. However two main differences appear, in comparison with simple ferromagnetic transitions: (i) the loop expansion yields a (negative) anomaly in the size dependence of the free energy, thereby lifting the lower critical dimension to a value greater than two (ii) the free energy is lowered by twisting the boundary conditions. This situation is common in spin glasses, reflecting the non-positivity of mode multiplicity in replica symmetry breaking, but its physical meaning is still unclear. [ABSTRACT FROM AUTHOR]

The relationship between extended structures, glassy dynamics and an underlying critical point is examined in the context of a lattice model of fluctuating lines. Monte Carlo simulations are used to construct an effective, coarse-grained dynamics for the “order parameter” near the critical point. Analysis of the effective dynamics reveals that the critical point is associated with diverging barriers leading to the observed Vogel-Fulcher divergence of the relaxation times. A direct connection is established between the presence of extended structures and the activated dynamics. [ABSTRACT FROM AUTHOR]

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse “transition” is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters (“double stars”). We analyze the thermodynamics of the system and the stability of the different equilibrium configurations against rotational symmetry breaking, and provide the global phase diagram. [ABSTRACT FROM AUTHOR]

Organic compounds exhibiting the smectic C phase are made of rod-like molecules that have dipolar groups with lateral components. We argue that the off-axis character of the lateral dipolar groups can account for tilt in layered smectics (SmC, SmC*, SmI etc.). We develop a mean-field theory of the smectic C phase based on a single-particle potential of the form UC ∝ sin(2θ)cosφ, consistent with the biaxial nature of the phase, where θ and φ are the polar and azimuthal angles, respectively. The hard-rod interactions that favour the smectic A phase with zero tilt angle are also included. The theoretical phase diagrams compare favourably with experimental trends. Our theory also leads to the following results: i) a first-order smectic C to smectic A transition above some value of the McMillan parameter α, leading to a tricritical point on the smectic C to smectic A transition line and ii) a first-order smectic C to smectic C transition over a very small range of values of the model parameters. We have also extended the theory to include the next higher-order term in the tilting potential and to include the effect of different tilt angles for the molecular core and the chain in the SmC phase. [ABSTRACT FROM AUTHOR]

In this paper we investigate the conformation statistics of a Gaussian chain embedded in a medium of finite size, in the presence of quenched random obstacles. The similarities and differences between the case of random obstacles and the case of a Gaussian random potential are elucidated. The connection with the density of states of electrons in a metal with random repulsive impurities of finite range is discussed. We also interpret the results obtained in some previous numerical simulations. [ABSTRACT FROM AUTHOR]

We test the influence of the Coulomb interaction on the thermodynamic and cluster generation properties of a system of classical particles described by different lattice models. Numerical simulations show that the Coulomb interaction produces essentially a shift in temperature of quantities like the specific heat but not qualitative changes. We also consider a cellular model. The thermodynamic properties of the system are qualitatively unaltered. [ABSTRACT FROM AUTHOR]

The possibility of microphase separation at two different length scales in monodisperse AB block copolymer melts consisting of a homopolymer A block and either a linear alternating AB copolymer block (poly( A)m- block-poly( B- alt - A)n) or an AB comb copolymer block poly( A)m- block-poly( A- graft- B)n, is investigated. An analysis of the structure factor reveals that in the parameter space of n and m three different cases can be distinguished: I) The structure factor has only one minimum corresponding to the short length scale ( i.e. the characteristic length of the repeating unit of the alternating or comb block). II) The structure factor has only one minimum corresponding to the long length scale (the characteristic length of the blocks). III) Two minima are present leading to a competition between microphase separation at the short and the long length scale. Depending on the choice of n and m, one of these three possibilities will occur. [ABSTRACT FROM AUTHOR]

In this study we develop a theory of tracer diffusion in 2D lattice-gas systems with strongly repulsive nearest neighbor interactions. The study is performed for a square lattice in the vicinity of half monolayer coverage. In this case the lattice gas forms a highly-ordered c phase. The adatom kinetics is reduced to the problem of random walks of long-living structural defects. The correlated motion of tracer-defect pairs is considered. Equations for correlation functions of tracer-vacancy, tracer-excessive adatoms and tracer-dimer pairs are derived and solved in terms of microscopic jump probabilities of defects. The solutions are exact in the case of dominant single defect transport mechanisms. In the case of dimer transport we applied the approximation of short-range correlation length. The values obtained for the correlation factor are in good agreement with the results of computer simulations in the over-stoichiometric range, while for sub-stoichiometric coverages the agreement is not very good. [ABSTRACT FROM AUTHOR]

The similarity in the thermodynamic properties of two completely different theoretical models for the helix-coil transition is examined critically. The first model is an all-atomic representation for a poly-alanine chain, while the second model is a minimal helix-forming model that contains no system specifics. Key characteristics of the helix-coil transition, in particular, the effective critical exponents of these two models agree with each other, within a finite-size scaling analysis. [ABSTRACT FROM AUTHOR]

K0.88Rb0.12TiOPO4 and K0.465Rb0.535TiOPO4 solid solutions of the potassium titanyl phosphate (KTiOPO4, space group Pna21) family, are described at 293, 473, 673, 873 and at 973 K. Their high resolution structures are obtained by using accurate single-crystal X-ray diffraction techniques at high resolution, (sin Å-1. Large anharmonic motion of alkaline ions increasing with temperature allows the evolution of the rubidium and potassium ions repartition in the two alkaline sites versus temperature. To describe this motion inducing ionic conductivity phenomenon and to determine accurately the order-disorder evolution, two alkaline site refinement models are developed and discussed. A thermodynamic model, which uses a barrier-potential model, is also developed to specify the different interactions operating in the order-disorder evolution, and more generally interactions between alkaline ions and the framework. [ABSTRACT FROM AUTHOR]

We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined. [ABSTRACT FROM AUTHOR]

It is well-known that 1D systems with only nearest neighbour interaction exhibit no phase transition. It is shown that the presence of a small long range interaction treated by the mean field approximation in addition to strong nearest neighbour interaction gives rise to hysteresis curves of large width. This situation is believed to exist in spin crossover systems where by the deformation of the spin changing molecules, an elastic coupling leads to a long range interaction, and strong bonding between the molecules in a chain compound leads to large values for nearest neighbour interaction constants. For this interaction scheme an analytical solution has been derived and the interplay between these two types of interaction is discussed on the basis of experimental data of the chain compound which exhibits a very large hysteresis of 50 K above RT at 370 K. The width and shape of the hysteresis loop depend on the balance between long and short range interaction. For short range interaction energies much larger than the transition temperature the hysteresis width is determined by the long range interaction alone. [ABSTRACT FROM AUTHOR]

The semi-infinite axial next nearest neighbor Ising (ANNNI) model in the disordered phase is treated within the molecular field approximation, as a prototype case for surface effects in systems undergoing transitions to both ferromagnetic and modulated phases. As a first step, a discrete set of layerwise mean field equations for the local order parameter mn in the nth layer parallel to the free surface is derived and solved, allowing for a surface field H1 and for interactions JS in the surface plane which differ from the interactions J0 in the bulk, while only in the z-direction perpendicular to the surface competing nearest neighbor ferromagnetic exchange (J1) and next nearest neighbor antiferromagnetic exchange ( J 2) occurs. We show that for and temperatures in between the critical point of the bulk and the disorder line the decay of the profile is exponential with two competing lengths with while stays finite at . The amplitudes of these exponentials ( a is the lattice spacing) are obtained from boundary conditions that follow from the molecular field equations. For but , as well as at the Lifshitz point and in the modulated region , we obtain a modulated profile , where again the amplitude A and the phase can be found from the boundary conditions. As a further step, replacing differences by differentials we derive a continuum description, where the familiar differential equation in the bulk (which contains both terms of order and here) is supplemented by two boundary conditions, which both contain terms up to order . It is shown that the solution of the continuum theory reproduces the lattice model only when both the leading correlation length ( or , respectively) and the second characteristic length ( or the wavelength of the modulation , respectively) are very large. We obtain for a surface transition, with a two-dimensional ferromagnetic order occurring at a transition exceeding the transition of the bulk, and calculate the associated critical exponents within mean field theory. In particular, we show that at the Lifshitz point with while for the crossover exponent is . We also consider the “ordinary transition” and obtain the critical exponents and associated critical amplitudes (the latter are often singular when ). At the Lifshitz point, the exponents of the surface layer and surface susceptibilities take the values , while from scaling relations the surface “gap exponent” is found to be and the surface order parameter exponents are . Open questions and possible applications are discussed briefly. [ABSTRACT FROM AUTHOR]

Analytical expressions for chemical, jump, and tracer diffusion coefficients are obtained for interacting lattice gases on a square lattice. Strongly repulsive nearest neighbor interactions cause the formation of a highly-ordered c( ) state in the vicinity of half coverage. It is shown that only strongly correlated successive adatom jumps contribute to the particle flow. This allows to describe the adatom kinetics by considering an almost ideal lattice gas of defects. Two types of defects are considered, adatoms in the empty sublattice and vacancies in the filled sublattice of the c( ) ordered state. The diffusion equations for these defects are developed considering the generation and recombination of defects. In addition we have considered adatom transport caused by the motion of defect pairs (dimers). Dimer transport mechanism prevails in the high coverage region. The characteristic features of the various diffusion coefficients near half coverage are analyzed and discussed. The theory is compared with the results of sophisticated Monte-Carlo simulations which have been executed with the use of a fully parallelized algorithm on a Cray T3E (LC784-128). The agreement between theoretical and MC results is excellent if the motion of dimers at is taken into account. [ABSTRACT FROM AUTHOR]

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T- g plane, where g is the strength of the pairing interaction, for fixed variance J 2/ N of the random couplings Jij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g= g c( T) that ends at a tricritical point T 3=0.9807 J, g 3=5,8843 J, from where it becomes a first order transition line that meets the line of second order transitions at T c=0.9570 J that separates the NP and the SG phases. For T< T c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . [ABSTRACT FROM AUTHOR]

The effect of stiffness in a 2D living polymer system is investigated by Monte-Carlo simulation in a canonical ensemble. As the flexibility decreases, the mean chain contour length decreases and goes through a local maximum. The mean end to end square distance shows a non-monotonic behaviour due to the coil-to-rod transition and the decrease in chain contour length. Near the maximum of chain ordering in the bulk, the chain length distribution adapts itself to increase the configurational entropy. With the parameters used in this simulation, it seems that the effect of the stiffness for high stiffness is to decrease as in the isotropic case, since the ordering decreases again. [ABSTRACT FROM AUTHOR]

The simulation of a two-dimensional, broadly polydisperse, living polymers system at high concentration reveals an unusual conformational behaviour for the longer chains. Unlike in three dimensions, the longer chains are not swollen but are squeezed by the smaller chains. This observation is discussed in terms of a two dimensional solvent- polymer mixture whose solvent particules are larger than the polymer monomers. [ABSTRACT FROM AUTHOR]

We consider a system composed of a monodisperse charge-stabilized colloidal suspension in the presence of monovalent salt, separated from the pure electrolyte by a semipermeable membrane, which allows the crossing of solvent, counterions, and salt particles, but prevents the passage of polyions. The colloidal suspension, that is in a crystalline phase, is considered using a spherical Wigner-Seitz cell. After the Donnan equilibrium is achieved, there will be a difference in pressure between the two sides of the membrane. Using the functional density theory, we obtained the expression for the osmotic pressure as a function of the concentration of added salt, the colloidal volume fraction, and the size and charge of the colloidal particles. The results are compared with the experimental measurements for ordered polystyrene lattices of two different particle sizes over a range of ionic strengths and colloidal volume fractions. [ABSTRACT FROM AUTHOR]

We investigate kinetics of nematic-isotropic transition by solving the hydrodynamic equations for the nematic tensor order parameter and the fluid velocity in two space dimension ( x- y plane). Numerical results indicate that nematic directors tend to align parallel to the x- y plane when hydrodynamic flow is incorporated. Late stage growth exponents, for the correlation length and for the number of topological defects, are not significantly altered by hydrodynamic flow. However, in contrast to the case without flow, the relation holds well, which may indicate the validity of dynamical scaling for the case with hydrodynamic flow. [ABSTRACT FROM AUTHOR]

In present work we discuss the problem of introducing stochasticity into 3D atomistic kinetic mean-field simulations. As this is a new approach for simulating the time evolution of material systems, it should be positioned in the field of available methods. Compared to the most used stochastic techniques: while atomistic kinetic Monte Carlo (KMC) methods generate microstates of the system they simulate, stochastic kinetic mean-field (SKMF) seems to generate mesostates of the system during a finite time-window. Previously, strong interrelation have been found for the dispersion of composition fluctuations in ideal solutions between SKMF states and averaged KMC states. In present work we compare the statistical nature of fluctuations in the two approaches in case of equilibrium solid solutions with non-zero mixing energies. At the investigated high temperature cases we show how at a certain noise amplitude in SKMF the composition fluctuations can be related to results received by averaging a certain number of independent KMC states. Furthermore, the correlation between the neighboring sites, emerging because of the chemical interactions, shows the same statistical behavior in both methods as well. [ABSTRACT FROM AUTHOR]