Critical behavior of the random-field Ising model

We study the critical properties of the random field Ising model in general dimension d using high-temperature expansions for the susceptibility, \ensuremath{\chi}=${\ensuremath{\sum}}_{\mathit{j}}$ [〈${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}}$${\mathrm{\ensuremath{\sigma}}}_{\mathit{j}}$${\mathrm{〉}}_{\mathit{T}}$-〈${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}}$${\mathrm{〉}}_{\mathit{T}}$〈${\mathrm{\ensuremath{\sigma}}}_{\mathit{j}}$${\mathrm{〉}}_{\mathit{T}}$${]}_{\mathit{h}}$ and the structure factor, G=${\ensuremath{\sum}}_{\mathit{j}}$[〈${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}}$${\mathrm{\ensuremath{\sigma}}}_{\mathit{j}}$${\mathrm{〉}}_{\mathit{T}}$${]}_{\mathit{h}}$, where 〈${\mathrm{〉}}_{\mathit{T}}$ indicates a canonical average at temperature T for an arbitrary configuration of random fields and [${]}_{\mathit{h}}$ indicates an average over random fields. We treated two distributions of random fields, the bimodal in which each ${\mathit{h}}_{\mathit{i}}$=\ifmmode\pm\else\textpm\fi{}${\mathit{h}}_{0}$ and a Gaussian distribution in which each ${\mathit{h}}_{\mathit{i}}$ has variance ${\mathit{h}}_{0}^{2}$. We obtained series for \ensuremath{\chi} and G in the form ${\ensuremath{\sum}}_{\mathit{n}=1,15}$${\mathit{a}}_{\mathit{n}}$(g,d)(J/T${)}^{\mathit{n}}$, where J is the exchange constant and the coefficients ${\mathit{a}}_{\mathit{n}}$(g,d) are polynomials in g\ensuremath{\equiv}${\mathit{h}}_{0}^{2}$/${\mathit{J}}^{2}$ and in d. We assume that as T approaches its critical value, ${\mathit{T}}_{\mathit{c}}$, one has \ensuremath{\chi}\ensuremath{\sim}(T-${\mathit{T}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$ and G\ensuremath{\sim}(T-${\mathit{T}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}$. For dimensions above d=2 we find a range of values of g for which the critical exponents obtained from our series seem not to depend on g.