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We explicitly compute the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models at the upper critical behavior (for short and long range ϕn-theories) and below it. This allows us to check the scaling relations among these critical exponents obtained by analysing the complex singularities (Lee-Yang and Fisher zeroes) of these models. Moreover, we have obtained an explicit method to compute the ϙ exponent [defined by ξ ~ L(log L)ϙ] and, finally, we have found a new derivation of the scaling law associated with it. [ABSTRACT FROM AUTHOR]

A spin-glass transition occurs both within and outside of the limits of validity of mean-field theory for a diluted one-dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to changing the dimension in spin-glass short-range models. Using different finite-size scaling methods, evidence for a spin-glass transition is also found for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field. The application of a new method is discussed, which can be exported to systems in a magnetic field. [ABSTRACT FROM AUTHOR]

The article discusses the use of "Janus," a computing system based on field programmable gate arrays (FPGAs), to generate simulations for Monte Carlo statistical mechanics. Topics include a description of the Janus architecture, details of Monte Carlo procedures, the requisite software environment, and modifying Janus for spin-system simulations.

Working in and out of equilibrium and using state-of-the-art techniques we have computed the dynamic critical exponent of the three-dimensional Heisenberg model. By computing the integrated autocorrelation time at equilibrium, for lattice sizes L ≤ 64, we have obtained z = 2.033 (5). In the out-of-equilibrium regime we have run very large lattices (L ≤ 250) obtaining z = 2.04 (2) from the growth of the correlation length. We compare our values with that previously computed at equilibrium with relatively small lattices (L ≤ 24), with that provided by means a three-loops calculation using perturbation theory and with experiments. Finally we have checked previous estimates of the static critical exponents, η and ν, in the out-of-equilibrium regime. [ABSTRACT FROM AUTHOR]

We report on extensive numerical simulations of the three-dimensional Heisenberg model and its analysis through finite-size scaling of Lee-Yang zeros. Besides the critical regime, we also investigate scaling in the ferromagnetic phase. We show that, in this case of broken symmetry, the corrections to scaling contain information on the Goldstone modes. We present a comprehensive Lee-Yang analysis, including the density of zeros, and confirm recent numerical estimates for critical exponents. [ABSTRACT FROM AUTHOR]

We revisited, by means of numerical simulations, the one-dimensional bond diluted Levy Ising spin glasses outside the limit of validity of mean-field theories. In these models the probability that two spins at distance r interact (via disordered interactions, Jij= ±1) decays as r-p. We have estimated, using finite size scaling techniques, the infinite volume correlation length and spin glass susceptibility for p = 5/3 and p = 9/5. We have obtained strong evidence for divergences of the previous observables at a nonzero critical temperature. We discuss the behavior of the critical exponents, especially when approaching the value p = 2, corresponding to a critical threshold beyond which the model has no phase transition. Finally, we numerically study the model right at the threshold value p = 2. [ABSTRACT FROM AUTHOR]

We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L = 40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain Tc = 1.1019(29) for the critical temperature, v = 2.562(42) for the thermal exponent, η = -0.3900(36) for the anomalous dimension, and ω = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield α = -5.69(13), β =0.782(10), and γ =6.13(11). We also compute several universal quantities at Tc. [ABSTRACT FROM AUTHOR]

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out on the citizen supercomputer Ibercivis. Upon dilution, the pure model's first-order transition becomes of the second order at a tricritical point. We compute accurately the critical exponents at the tricritical point. As expected from the Cardy-Jacobsen conjecture, they are compatible with their random field Ising model counterpart. The conclusion is further reinforced by comparison with older data for the Potts model with four states. [ABSTRACT FROM AUTHOR]

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, stochastic stability, and overlap equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda-Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks. [ABSTRACT FROM AUTHOR]

Experiments on spin glasses can now make precise measurements of the exponent z(T) governing the growth of glassy domains, while our computational capabilities allow us to make quantitative predictions for experimental scales. However, experimental and numerical values for z(T) have differed. We use new simulations on the Janus II computer to resolve this discrepancy, finding a time-dependent z(T,tw), which leads to the experimental value through mild extrapolations. Furthermore, theoretical insight is gained by studying a crossover between the T=Tc and T=0 fixed points. [ABSTRACT FROM AUTHOR]

Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d=3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a dispersed metastate, supported on many thermodynamic states. [ABSTRACT FROM AUTHOR]

We first reproduce on the Janus and Janus II computers a milestone experiment that measures the spin-glass coherence length through the lowering of free-energy barriers induced by the Zeeman effect. Secondly, we determine the scaling behavior that allows a quantitative analysis of a new experiment reported in the companion Letter [S. Guchhait and R. Orbach, Phys. Rev. Lett. 118, 157203 (2017)]. The value of the coherence length estimated through the analysis of microscopic correlation functions turns out to be quantitatively consistent with its measurement through macroscopic response functions. Further, nonlinear susceptibilities, recently measured in glass-forming liquids, scale as powers of the same microscopic length. [ABSTRACT FROM AUTHOR]

We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy. [ABSTRACT FROM AUTHOR]

We revisit the universal behavior of crystalline membranes at and below the crumpling transition, which pertains to the mechanical properties of important soft and hard matter materials, such as the cytoskeleton of red blood cells or graphene. Specifically, we perform large-scale Monte Carlo simulations of a triangulated two-dimensional phantom network which is freely fluctuating in three-dimensional space. We obtain a continuous crumpling transition characterized by critical exponents which we estimate accurately through the use of finite-size techniques. By controlling the scaling corrections, we additionally compute with high accuracy the asymptotic value of the Poisson ratio in the flat phase, thus characterizing the auxetic properties of this class of systems. We obtain agreement with the value which is universally expected for polymerized membranes with a fixed connectivity. [ABSTRACT FROM AUTHOR]