arXiv 2104.024902021-04-06cond-mat.dis-nncond-mat.stat-mech

Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models

Valentin Anfray, Christophe Chatelain

发表信息：: Phys. Rev. B 103, 174207 (2021)
DOI：: 10.1103/PhysRevB.103.174207

英文摘要：

The random q-state quantum Potts model is studied on hypercubic lattices in dimensions 2 and 3 using the numerical implementation of the Strong Disorder Renormalization Group introduced by Kovacs and Igl{ó}i [Phys. Rev. B 82, 054437 (2010)]. Critical exponents $ν$, d f and $ψ$ at the Infinite Disorder Fixed Point are estimated by Finite-Size Scaling for several numbers of states q between 2 and 50. When scaling corrections are not taken into account, the estimates of both d f and $ψ$ systematically increase with q. It is shown however that q-dependent scaling corrections are present and that the exponents are compatible within error bars, or close to each other, when these corrections are taking into account. This provides evidence of the existence of a super-universality of all 2D and 3D random Potts models.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Universality and multifractal behaviour of spin-spin correlation functions in disordered Potts models

We report a transfer matrix study of the random bond $q-$state Potts model in the vicinity of the Ising model $q=2$. We draw attention to a precise determination of magnetic scaling dimensions in order to compare with perturbative results. Universality is checked by the computation of the spin-spin correlation function decay exponent obtained with different types of probability distributions of the coupling strengths. Our numerical data, compared to perturbative results for the second moment of the correlation function, obtained with both replica symmetry and replica symmetry breaking schemes,…

2000-04-12cond-mat.dis-nncond-mat.stat-mech

Phase diagram and critical exponents of a Potts gauge glass

The two-dimensional q-state Potts model is subjected to a Z_q symmetric disorder that allows for the existence of a Nishimori line. At q=2, this model coincides with the +/- J random-bond Ising model. For q>2, apart from the usual pure and zero-temperature fixed points, the ferro/paramagnetic phase boundary is controlled by two critical fixed points: a weak disorder point, whose universality class is that of the ferromagnetic bond-disordered Potts model, and a strong disorder point which generalizes the usual Nishimori point. We numerically study the case q=3, tracing out the phase diagram and…

2001-06-13cond-mat.dis-nncond-mat.stat-mech

Universality of the Crossing Probability for the Potts Model for q=1,2,3,4

The universality of the crossing probability $π_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for percolation $q=1$. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction $π_{hs}$ has universal form $π_{hs}=A(q) Q(z)$ for $q=1,2,3,4$…

2003-09-20cond-mat.dis-nn

Scaling of crossing probabilities for the q-state Potts model at criticality

We present study of finite-size scaling and universality of crossing probabilities for the $q$-state Potts model. Crossing probabilities of the Potts model are similar ones in percolation problem. We numerically investigated scaling of $π_{s}$ - the probability of a system to percolate only in one direction for two-dimensional site percolation, the Ising model, and the q-state Potts model for $q=3,4,5,6,8,10$. We found the thermal scaling index $y= \frac{1}ν$ for $q<4$. In contrast, $y \ne \frac{1}ν$ for $q=4$.

2000-05-25cond-mat.dis-nncond-mat.stat-mech

Critical Behaviour of Random Bond Potts Models: A Transfer Matrix Study

We study the two-dimensional Potts model on the square lattice in the presence of quenched random-bond impurities. For q>4 the first-order transitions of the pure model are softened due to the impurities, and we determine the resulting universality classes by combining transfer matrix data with conformal invariance. The magnetic exponent beta/nu varies continuously with q, assuming non-Ising values for q>4, whereas the correlation length exponent nu is numerically consistent with unity. We present evidence for the correctness of a formerly proposed phase diagram, unifying pure, percolative and…

1997-11-26cond-mat.dis-nncond-mat.stat-mech

Quantum criticality in the 2d quasiperiodic Potts model

Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and paramagnetic phases in the quasiperiodic $q$-state Potts model in $2+1d$. Using a controlled real-space renormalization group approach, we find that the critical behavior is largely independent of $q$, and is controlled by an infinite-quasiperiodicity fixed point. The correlation length exponent is found to be $ν=1$, saturating a modified version of the Harris-Luc…

2020-08-26cond-mat.dis-nncond-mat.stat-mechcond-mat.str-el

更多相关论文收起更多论文

Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond 8-state Potts Model

The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and deduce the corresponding critical exponents at the random fixed point using standard finite-size scaling techniques. The scaling laws are suitably satisfied. We find that a belonging of the model to the 2D Ising model universality class can be conclusively ruled out, and the dimensions of the relevant bulk and surface scaling fields are found to take the valu…

1998-01-06cond-mat.dis-nncond-mat.stat-mech

Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models

As is known, at the Gibbs-Boltzmann equilibrium, the mean-field $q$-state Potts model with a ferromagnetic coupling has only a first order phase transition when $q\geq 3$, while there is no phase transition for an antiferromagnetic coupling. The same equilibrium is asymptotically reached when one considers the continuous time evolution according to a Glauber dynamics. In this paper we show that, when we consider instead the Potts model evolving according to a discrete-time dynamics, the Gibbs-Boltzmann equilibrium is reached only when the coupling is ferromagnetic while, when the coupling is a…

2013-04-02cond-mat.dis-nncond-mat.stat-mechphysics.soc-ph

Phase transitions in two-dimensional random Potts models

The influence of uncorrelated, quenched disorder on the phase transition of two dimensional Potts models will be reviewed. After an introduction where the conditions of relevance of quenched randomness on phase transitions are exemplified by experimental measurements, the results of perturbative and numerical investigations in the case of the Potts model will be presented. The Potts model is of particular interest, since it can have in the pure case a second-order or a first-order transition, depending on the number of states per spin. In 2D, transfer matrix calculations and Monte Carlo simula…

2002-07-17cond-mat.dis-nn

The Super-Potts glass: a new disordered model for glass-forming liquids

We introduce a new disordered system, the Super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pair-wise interactions. Its exact solution on a completely connected lattice demonstrates that for large enough M it belongs to the class of mean-field systems solved by a one step replica symmetry breaking Ansatz. Numerical simulations by the parallel tempering technique show that in three dimensions it displays a phenomenological behaviour similar to the one of glass-forming liquids. The …

2015-01-14cond-mat.dis-nncond-mat.stat-mech

Monte Carlo Studies of Three-Dimensional Bond-Diluted Ferromagnets

In this report we give an overview on recent results obtained from extensive Monte Carlo (MC) computer simulations of the 3D 2-state (Ising) and 4-state Potts models with bond-dilution. The motivation to study the 4-state Potts model derives from the fact that, in the pure case, this model is known to exhibit a fairly strong first-order transition, such that a disorder-induced softening to a second-order transition would give clear support of the theoretical expectations. Modeling the disorder by bond-dilution enables in the Ising case a test of the expected universality with respect to the ty…

2002-12-19cond-mat.dis-nncond-mat.stat-mech

长程键无序Potts模型的磁指数

Magnetic exponent for the long-range bond disordered Potts model

本文通过扰动共形场论计算二维Potts模型在长程键无序下的磁学扇区临界行为，得到自旋标度维度修正，并与蒙特卡洛模拟对比，证实长程与短程普适类的交叉。

2024-07-18cond-mat.dis-nnhep-th

Universality aspects of the d=3 random-bond Blume-Capel model

The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that, the second-order transition emerging under bond randomness from the first-or…

2012-05-31cond-mat.dis-nncond-mat.stat-mech

Universality and Quantum Criticality in Quasiperiodic Spin Chains

Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems as well as disordered ones. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization group transformation. These discrete sequences are therefore fixed points of a \emph{functional} renormalizat…

2019-08-07cond-mat.dis-nncond-mat.stat-mechcond-mat.str-el

Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out in 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.

2012-11-17cond-mat.dis-nncond-mat.stat-mech

Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical physics of disordered systems and computer science has brought new light into the realm of computational complexity theory, by introducing the notion of clustering of solutions, related to replica symmetry breaking. However, the class of problems in which clustering has been studied often involve discrete degrees of freedom: standard random CSPs are random K-SAT…

2017-04-29cond-mat.dis-nn