Coherent anomaly method for classical Heisenberg model

Abstract

The power series coherent anomaly method is applied to study the critical properties of a classical Heisenberg model. The values of true critical temperature T c ∗ are obtained. Using these results the estimation of critical exponent γ for the zero-field static susceptibility has been made. The results for T c ∗ are in good agreement with those obtained from the ratio method and the Padé approximant analysis of the direct susceptibility series. But the results for γ are found to be different. It is seen that γ for bcc and fcc lattices is approximately equal to 4 3 , while for the sc lattice γ 2> 4 3 , in disagreement with the mean experimental value of 4 3 . With the proposal of a possible correction due to confluent singularities for sc model we obtain the following expression for susceptibility: χ = a(1 − t c ) − 4 3 [1 + B(1 − t c ) Δ∗] , with x c = x c x c ∗ , x c = J k B T c , k B being the Boltzmann constant, J the nearest-neighbour exchange constant, T cc the critical temperature. B and a are numerical constants. Δ ∗ , the confluent correction has been found to be 0.42 for the sc lattice and non-existent in bcc and fcc lattices.