Ising model universality for two-dimensional lattices

Abstract

We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices of Delaunay type with up to 80 000 sites. By applying reweighting techniques and finite-size scaling analyses to time-series data near criticality, we obtain unambiguous support that the critical exponents for the random lattice agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model. *

Critical behavior of the spin-3/2 Blume-Capel model on a random two-dimensional lattice

“…A linear fit of these data gives β/ν = 0.331(9) from the magnetization and γ/ν = 1.467(9) from the susceptibility which should be compared to β/ν = 0.125 and γ/ν = 1.75 obtained for a regular 2D lattice. The specific heat can also be analysed in this case but, as it happens in other models [21,23], we cannot find a clear unambiguous support for a definite scaling. Fig.…”

“…To achieve the desired accuracy of the data in reasonable computer time we applied the single-cluster hybrid algorithm [18] to update the spins and furthermore made extensively use of the re-weighting technique [19]. Previous studies of connectivity disorder focusing mainly on 2D lattices have been realized by Monte Carlo simulations of qstate Potts models on quenched random lattices of VoronoiDelaunay type for q = 2 [20][21][22], q = 3 [23] and q = 8 [24,25]. In particular, it has been shown that for q = 2 [20][21][22] and q = 3 [23] the critical exponents are the same as those for the model on a regular 2D lattice.…”

“…Previous studies of connectivity disorder focusing mainly on 2D lattices have been realized by Monte Carlo simulations of qstate Potts models on quenched random lattices of VoronoiDelaunay type for q = 2 [20][21][22], q = 3 [23] and q = 8 [24,25]. In particular, it has been shown that for q = 2 [20][21][22] and q = 3 [23] the critical exponents are the same as those for the model on a regular 2D lattice. This is indeed a surprising result since the relevance criterion of the Delaunay triangulations reduces to the well known Harris criterion such that disorder of this type should be relevant for any model with positive specific heat exponent [26].…”

A multicanonical algorithm for SU (3) pure gauge theory

“…They agree reasonably with those obtained in ref. [9] for periodic boundary conditions. However, there is no plateau for the probabilities around S min L .…”

Nonlocal Monte Carlo algorithms for statistical physics applications

“…Randomly diluted ferromagnetic systems such as the 2D random bond Ising [63,64] and Potts [65] model or the 3D site diluted Ising model [66] pose no new problems, and simulations on random lattices [67] or graphs [68] and fluctuating Regge triangulations [69] of quantum gravity are also straightforward. For systems with competing ferro-and antiferromagnetic interactions and frustrations, on the other hand, it is not guaranteed that a straightforward cluster formulation leads to improvements even though this would be a valid algorithm.…”