We investigate the phase structure of the d-dimensional q-state Potts models on lattice by the variational cumulant expansion (VCE) approach, we calculate the internal energy and specific heat for this model. Specially, we give the results for 2-dimensional q = 4,5,6 states Potts models. A comparison with Monte Carlo (MC) data is also presented. Our formalism can give the results for Potts models in any dimensionality d and any states q straightforwardly.
The variational cumulant expansion is extended to d-dimensional U(]) gauge .theory with radially active Higgs fields in the fundamental representation. The phase structures are given for d = 3 and d = 4 cases. A comparison with Monte Carlo and mean field results is also presented.
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