Evidence Against Spin-Glass Order in the Two-Dimensional Random-Bond Ising Model

Abstract

By recursive methods, numerically exact free energies are calculated for $L\times L$ Ising lattices with bonds of randomly chosen sign, with $6<~L<~18$. Ground states of these systems are identified, and the response to ordering fields is studied. By performing Monte Carlo simulations for precisely the same systems we are able to unambiguously distinguish nonequilibrium phenomena from equilibrium properties. The $L$ dependence of our results suggests that there is no nonzero spin-glass order parameter for $L\to \infty$.