Exact solution of the three-state generalized double-chain Potts model

Abstract

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.