Variat ional-Cumulant Expansion on the Five-State Clock Model

The phase transition of the 5-state dock model has been studied by standard variationalcumulant expansion (VCE) method. We calculated the fiee energy (F) and the internal energy (E) to the fourth order approximation and the specific heat (C) to the third order approximation with the trial action of one variational parameter. The position of the phase transition point given above is in agreement with the results of the Monte Carlo (MC). We also calculated the model to the third order approximation with the trial action of two variational parameters. The comparison of the results for one variational parameter with that for two is given. From this, we can see how the choice of the trial action affects the result and the trial action must be equivalent to the action of the system. All above has shown that the VCE is convergent in the calculation of the 5-state clock model.