Dynamics of spin systems with correlated random fields

Abstract

We study the dynamic critical behavior of spin systems in the presence of quenched random magnetic fields with long-range correlations of the type ${[h(0)h(R)]}_{\mathrm{av}}\ensuremath{\sim}{R}^{\ensuremath{-}(d\ensuremath{-}\ensuremath{\theta})}$. We assume that the dynamics is described by a Langevin equation without conservation of the order parameter. It is shown in both the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}$ expansion ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}=6+\ensuremath{\theta}\ensuremath{-}d$) to order ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}}^{2}$ and $\frac{1}{N}$ expansion to leading order for $4+\ensuremath{\theta}ldl6+\ensuremath{\theta}$ that the dynamic critical exponent $z$ can be expressed in terms of static exponent $\ensuremath{\eta}$ as $z=2+g(\ensuremath{\theta})\ensuremath{\eta}$. The dynamic scaling form of the spin-spin correlation function at $T={T}_{c}$ is obtained to order ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}}^{2}$.