Thermodynamics and Low-Temperature Spectrum of the Three-State Potts Model

Srinandan Dasmahapatra, Rinat Kedem, Barry M. McCoy

Rinat Kedem

Pavel Khrapov, G. E. Skvortsov

An exact analytical solution of generalized three-state double-chain Potts model with multi-spin interactions which are invariant under cyclic shift of all spin values is obtained. The partition function in a finite cyclically closed strip of length L, as well as the free energy, internal energy, entropy and heat capacity in thermodynamic limit are calculated using transfer-matrix method. Partial magnetization and susceptibility are suggested as the generalization of usual physical characteristics of a system. Proposed model can be interpreted as a generalized version of standard Potts model (which has Hamiltonian expressed through Kronecker symbols) and clock model (with Hamiltonian expressed through cosines). Considering a particular example of the model with plenty of forces, model's ground states are found, figures of its thermodynamic characteristics and discussed their behaviour at low temperature are shown.

A. K. Kwaśniewski

В. И. Зиненко

Abstract The thermodynamics of the q‐state Potts model is calculated by the cluster approximation. With two, three, and four particles as the basic cluster the free energy is obtained for any q. It is found that the transition is of the first order for all two‐dimensional and three‐dimensional Potts models. In the case of planar lattices for q = 3 and q = 4 it is found that the critical point approaches the Curie‐Weiss temperature but the discontinuity of the order parameter remains almost equal to that obtained by the mean‐field approximation.

Francesco Fucito, Angelo Vulpiani