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

TL;DR

This paper presents an exact analytical solution for a generalized three-state double-chain Potts model with multi-spin interactions, calculating key thermodynamic properties and exploring its ground states and low-temperature behavior.

Contribution

It introduces a new exactly solvable model extending the standard Potts and clock models, with detailed thermodynamic analysis and ground state characterization.

Findings

Exact partition function and thermodynamic quantities derived

Ground states identified for specific force configurations

Thermodynamic behavior analyzed at low temperatures

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.