Spin-glass order parameter of the random-field Ising model

Abstract

The Edwards-Anderson spin-glass order parameter $Q$ is calculated in the critical region for the randomfield Ising model. It is proportional to ${h}^{\frac{(d\ensuremath{-}2+\ensuremath{\eta})}{(1\ensuremath{-}\frac{\ensuremath{\eta}}{2})}}$ in $d$ dimensions for a root-mean-square random field $h$ and critical exponent $\ensuremath{\eta}$. Thus $Q$ approaches zero as $h\ensuremath{\rightarrow}0$, whereas simple linearized theory predicts it to diverge at the critical point of the pure system. The results are exact to order ${h}^{4}$ and in agreement with scaling theories. Numerical values are given both for $Q$ and the amplitude of the Lorentzian-squared structure factor.