One-dimensional $q$-state modified Potts model and its thermodynamic functions

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 $q$-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 $T \to 0$ and $T \to \infty$. The findings contribute to a deeper understanding of the model's thermodynamic characteristics and highlight its potential applications across various disciplines.