Correlation of fluctuations in the Blume-Capel model

Abstract

Using a 1/z expansion we study the correlation of fluctuations in a spin-1 Ising model with anisotropy. Previously, the 1/z expansion has been applied only to the second-order phase transitions of ferromagnets and granular superconductors. By imposing conditions on the free energy F and the parameter x=1-〈${\mathit{S}}_{1\mathit{z}}^{2}$〉, we use the 1/z technique to examine both the first- and second-order parts of the Blume-Capel phase diagram. In agreement with many numerical simulations and experiments on $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures, the value of x at the tricritical point is not shifted from its mean-field value of 2/3 to order 1/z. On the other hand, the tricritical values of the anisotropy parameter A and of the transition temperature ${\mathit{T}}_{\mathit{c}}$ are altered by the correlation of fluctuations. At least to order 1/z, all the derivatives of ${\mathit{T}}_{\mathit{c}}$ are continuous across the tricritical point.