Exact solution for one-dimensional spin models with Markov property

TL;DR

This paper presents an exact method for solving one-dimensional spin models with Markov properties by expressing free energy in terms of bond concentrations and minimizing it, demonstrated on a dilute Ising chain.

Contribution

The paper introduces an exact solution approach for 1D spin models with Markov properties, linking free energy minimization to bond concentrations.

Findings

Exact free energy expression in terms of bond concentrations

Solution applied to dilute Ising chain with impurities

Method enables precise analysis of 1D spin systems

Abstract

For one-dimensional spin and pseudospin models that allow mapping to a Markov chain, the free energy of the system at a finite temperature can be expressed in terms of bond concentrations. Minimizing the free energy function makes it possible to obtain an exact solution of a statistical model. A dilute Ising chain with interacting impurities is considered as an example.