Coherent anomaly method for classical Heisenberg model

The power series coherent anomaly method is applied to study the critical properties of a classical Heisenberg model. The values of true critical temperature Tc∗ are obtained. Using these results the estimation of critical exponent γ for the zero-field static susceptibility has been made. The results for Tc∗ 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 43, while for the sc lattice γ 2> 43, in disagreement with the mean experimental value of 43. With the proposal of a possible correction due to confluent singularities for sc model we obtain the following expression for susceptibility: χ = a(1 − tc)−43[1 + B(1 − tc)Δ∗], with xc = xcxc∗, xc = JkBTc, kB being the Boltzmann constant, J the nearest-neighbour exchange constant, Tcc 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.