CRITICAL-BEHAVIOR OF THE RANDOM-FIELD ISING-MODEL

We study the critical properties of the random field Ising model in ge neral dimension d using high-temperature expansions for the susceptibi lity, chi=Sigma(j)[[sigma(i) sigma(j)](T)-[sigma(i)](T)[sigma(j)](T)]( h) and the structure factor, G = Sigma(j)[[sigma(i) sigma(j)](T)](h), where [](T) indicates a canonical average at temperature T for an arbi trary configuration of random fields and [](h) indicates an average ov er random fields. We treated two distributions of random fields, the b imodal in which each h(i)=+/-h(0) and a Gaussian distribution in which each h(i) has variance h(0)(2). We obtained series for chi and G in t he form Sigma(n)=(1,15)a(n)(g,d)(J/T)(n), where J is the exchange cons tant and the coefficients a(n)(g,d) are polynomials in g equivalent to h(0)(2)/J(2) and in d. We assume that as T approaches its critical va lue, T-c, one has chi similar to(T-T-c)(-gamma) and G similar to(T-T-c )(-<(gamma)over bar>). For dimensions above d=2 we find a range of val ues of g for which the critical exponents obtained from our series see m not to depend on g. For large values of g our results show a g depen dence which is attributable to either a tricritical point or a first-o rder transition. All our results for critical exponents suggest that < (gamma)over bar>=2 gamma, in agreement with the two-exponent scaling p icture. In addition we have also constructed series for the amplitude ratio, A = (G/chi(2))(T-2)/(gJ(2)). We find that A approaches a consta nt value as T --> T-c (consistent with <(gamma)over bar>=2 gamma) with A approximate to 1. It appears that A is somewhat larger for the bimo dal than for the Gaussian model, in agreement with a recent analysis a t high d.