Monte Carlo simulation of the two-dimensional random (±J) Ising model

Abstract

A Monte Carlo simulation of the two-dimensional random ($\pm J$) Ising model has characterized the equilibrium and dynamic behavior of the model. The spin-glass correlation length diverges algebraically with absolute temperature. The equilibration time obeys an Arrhenius law at low temperature. There is a "phase transition at zero temperature" and a glass transition at finite temperature. In the spin-glass frequency ($f$) regime the noise power spectrum is proportional to $\frac{1}{f^{(1+\alpha )}}$ with $\alpha =0.28\mathrm{}$.