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February 6, 2026Физика металлов и металловедение / Physics of Metals and Metallography0 citations

The Exact Solution of One-Dimensional Spin Models With the Markov Property

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YPY. D. Panov

Key Points

  • The aim is to find the exact solution of one-dimensional spin models using the Markov property and analyzing free energy.
  • Analyzed one-dimensional spin and pseudospin models.
  • Mapped the models to a Markov chain framework.
  • Expressed free energy as a function of bond concentrations.
  • Minimized free energy to determine exact solutions.
  • Obtained exact solutions for the Potts model and dilute Ising chain.
  • Demonstrated the relationship between free energy and bond configurations.

Abstract

For one-dimensional spin and pseudospin models that can be mapped to a Markov chain, the free energy of the system at finite temperature can be expressed as a function of bond concentrations. By minimizing the free energy, we can obtain an exact solution for the statistical model. As examples, we consider the one-dimensional Potts model and the dilute Ising chain with interacting impurities.

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Cite This Study

Y. D. Panov (2025) studied this question.

synapsesocial.com/papers/698586118f7c464f23009e45https://doi.org/10.7868/s3034621525080065
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