The critical exponents of the two-dimensional Ising spin glass revisited: Exact Ground State Calculations and Monte Carlo Simulations

TL;DR

This study precisely determines critical exponents of the 2D Ising spin glass at zero temperature using exact ground state calculations and Monte Carlo simulations, providing new insights into its critical behavior.

Contribution

It offers the first comprehensive determination of multiple critical exponents for the 2D Ising spin glass at T→0 using combined computational methods.

Findings

Stiffness exponent y = -0.281 ± 0.002

Magnetic exponent δ = 1.48 ± 0.01

Chaos exponent ζ = 1.05 ± 0.05

Abstract

The critical exponents for $T\to0$ of the two-dimensional Ising spin glass model with Gaussian couplings are determined with the help of exact ground states for system sizes up to $L=50$ and by a Monte Carlo study of a pseudo-ferromagnetic order parameter. We obtain: for the stiffness exponent $y(=\theta)=-0.281\pm0.002$, for the magnetic exponent $\delta=1.48 \pm 0.01$ and for the chaos exponent $\zeta=1.05\pm0.05$. From Monte Carlo simulations we get the thermal exponent $\nu=3.6\pm0.2$. The scaling prediction $y=-1/\nu$ is fulfilled within the error bars, whereas there is a disagreement with the relation $y=1-\delta$.