Finite-size scaling in two-dimensional Ising spin glass models

TL;DR

This paper investigates the finite-size scaling behavior of two-dimensional Ising spin-glass models, confirming universality class membership and analyzing the scaling limit with implications for crossover temperature behavior.

Contribution

It provides a detailed analysis of finite-size scaling in 2D Ising spin glasses, confirming universality and asymptotic scaling laws for different disorder distributions.

Findings

Finite-size scaling holds asymptotically in the +-J model.

Models belong to the same universality class.

Crossover temperature scales as T_c(L) ~ L^(-theta_S) with theta_S ≈ 0.5.

Abstract

We study the finite-size behavior of two-dimensional spin-glass models. We consider the +-J model for two different values of the probability of the antiferromagnetic bonds and the model with Gaussian distributed couplings. The analysis of renormalization-group invariant quantities, the overlap susceptibility, and the two-point correlation function confirms that they belong to the same universality class. We analyze in detail the standard finite-size scaling limit in terms of TL^(1/nu) in the +-J model. We find that it holds asymptotically. This result is consistent with the low-temperature crossover scenario in which the crossover temperature, which separates the universal high-temperature region from the discrete low-temperature regime, scales as T_c(L) ~ L^(-theta_S) with theta_S \approx 0.5.