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Phase Transitions

One-dimensional 3-state and 4-state standard Potts models in magnetic field

Felix A. Kassan-Ogly

Published Feb 1, 2000• 10 citations
Publisher

Abstract

The exact solutions for 3-state and 4-state standard Potts models in external magnetic field are obtained within the framework of the Kramers-Wannier transfer matrix. The explicit analytical expressions for thermodynamic quantities such as magnetization, magnetic susceptibility and specific heat are derived and analysed at length as functions of temperature and magnetic field.

DOI
10.1080/01411590008228976

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The exact solutions for 3-state and 4-state standard Potts models in external magnetic field are obtained within the framework of the Kramers-Wannier transfer matrix. The explicit analytical expressions for thermodynamic quantities such as magnetization, magnetic susceptibility and specific heat are derived and analysed at length as functions of temperature and magnetic field.
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Since its introduction, the Potts model has gained widespread popularity across various fields due to its diverse applications. Even minor advancements in this model continue to captivate scientists worldwide, and small modifications often intrigue researchers from different disciplines. This paper investigates a one-dimensional qqq-state modified Potts model influenced by an external magnetic field. By leveraging the transfer matrix method, exact expressions are derived for key thermodynamic quantities, including free energy, entropy, magnetization, susceptibility, and specific heat capacity. Numerical analyses explore how these thermodynamic functions vary with relevant parameters, offering insights into the system's behavior. Additionally, the asymptotic properties of these quantities are examined in the limiting cases T→0T \to 0T→0 and T→∞T \to \inftyT→∞. The findings contribute to a deeper understanding of the model's thermodynamic characteristics and highlight its potential applications across various disciplines.
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