Evidence for two exponent scaling in the random field Ising model.

Abstract

Novel methods were used to generate and analyze new 15 term high temperature series for both the (connected) susceptibility \ensuremath{\chi} and the structure factor (disconnected susceptibility) ${\mathrm{\ensuremath{\chi}}}_{\mathit{d}}$ for the random field Ising model with dimensionless coupling K=J/kT, in general dimension d. For both the bimodal and the Gaussian field distributions, with mean square field ${\mathit{J}}^{2}$g, we find that (${\mathrm{\ensuremath{\chi}}}_{\mathit{d}}$-\ensuremath{\chi})/${\mathit{K}}^{2}$g${\mathrm{\ensuremath{\chi}}}^{2}$=1 as T\ensuremath{\rightarrow}${\mathit{T}}_{\mathit{c}}$(g), for a range of [${\mathit{h}}^{2}$]=${\mathit{J}}^{2}$g and d=3,4,5. This confirms the exponent relation \ensuremath{\gamma}\ifmmode\bar\else\textasciimacron\fi{}=2\ensuremath{\gamma} (where ${\mathrm{\ensuremath{\chi}}}_{\mathit{d}}$\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}$, \ensuremath{\chi}\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$, t=T-${\mathit{T}}_{\mathit{c}}$) providing that random field exponents are determined by two (and not three) independent exponents. We also present new accurate values for \ensuremath{\gamma}.