Ng. Fazleev et al., STUDY OF CRITICAL PROPERTIES OF THE POTTS-MODEL BY THE MODIFIED VARIATIONAL CUMULANT EXPANSION METHOD, Journal of applied physics, 76(10), 1994, pp. 6347-6349
The modified variational cumulant expansion (VCE) method valid for the
whole temperature range and for arbitrary fields is developed to stud
y the critical properties of the general q-state Potts model used to s
timulate various magnetic systems. The series expansion is generated d
irectly in terms of the Potts Hamiltonian. The free energy and the int
ernal energy are calculated up to the third-order cumulant terms for t
he d-dimensional hypercubic q-state Potts model. The expression for th
e critical temperature T-c is derived in a closed form which allows to
determine T-c up to arbitrary order cumulant terms. The modified VCE
method eliminates the unphysical first-order phase transition at the m
ean-field critical point in the internal energy of the Potts model whi
ch plagues the conventional VCE method.