Thermodynamic study of 3D XY model and Heisenberg model by analytical method

With Variational-Cumulant Expansion method, the specific heat and spontaneous magnetization of 3D classical XY model and Heisenberg model are calculated respectively up to the 5th and 4th order. The variational parameter is determined both by the Main Value method and by the accumulation point method. It is shown that the specific heat curve and the magnetization curve obtained by the accumulation point method are in better agreement with the MC results. The critical point T-c and critical exponent beta* are also calculated for the XY model.