Low-temperature behavior of two-dimensional Gaussian Ising spin glasses

TL;DR

This study uses advanced Monte Carlo simulations to analyze the low-temperature thermodynamic behavior of two-dimensional Gaussian Ising spin glasses, confirming a zero critical temperature and an algebraic divergence of the correlation length.

Contribution

It provides the first detailed thermodynamic analysis confirming the zero critical temperature and linking the correlation length exponent to the domain-wall exponent in 2D Gaussian Ising spin glasses.

Findings

Confirmed $T_c=0$ for the model

Found algebraic divergence of correlation length with exponent $ u$

Results compatible with domain-wall and droplet exponent $ heta \

Abstract

We perform Monte Carlo simulations of large two-dimensional Gaussian Ising spin glasses down to very low temperatures $\beta=1/T=50$. Equilibration is ensured by using a cluster algorithm including Monte Carlo moves consisting of flipping fundamental excitations. We study the thermodynamic behavior using the Binder cumulant, the spin-glass susceptibility, the distribution of overlaps, the overlap with the ground state and the specific heat. We confirm that $T_c=0$. All results are compatible with an algebraic divergence of the correlation length with an exponent $\nu$. We find $-1/\nu=-0.295(30)$, which is compatible with the value for the domain-wall and droplet exponent $\theta\approx-0.29$ found previously in ground-state studies. Hence the thermodynamic behavior of this model seems to be governed by one single exponent.