Previously, we proposed a long range mean field (LRMF) method to simplify the Hamiltonian of a one-dimensional (1D) chain with 1/r Coulomb repulsive interactions to study the vacancy ordering transitions in quasi-1D materials such as KCu7−xS4. We used a self-consistent (SC) method that...

Seven coefficients in the high temperature series expansions for the zero-field susceptibility and the specific heat are derived for the planar classical Heisenberg model with biquadratic interactions. The critical temperatures and the susceptibility exponents are determined for cubic lattices.

The quadrupole phase transition of a planar classical Heisenberg model with biquadratic interactions is investigated by the high-temperature series expansion method. From the quadrupole susceptibility series the critical temperatures and the critical exponents are determined for cubic lattices.