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

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 $y(=θ)=-0.281\pm0.002$, for the magnetic exponent $δ=1.48 \pm 0.01$ and for the chaos exponent $ζ=1.05\pm0.05$. From Monte Carlo simulations we get the thermal exponent $ν=3.6\pm0.2$. The scaling prediction $y=-1/ν$ is fulfilled within the error bars, whereas there is a disagreement with the relation $y=1-δ$.