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Since its introduction, the Potts model has gained widespread popularityacross various fields due to its diverse applications. Even minor advancementsin this model continue to captivate scientists worldwide, and smallmodifications often intrigue researchers from different disciplines. This paperinvestigates a one-dimensional \(q\)-state modified Potts model influenced byan external magnetic field. By leveraging the transfer matrix method, exactexpressions are derived for key thermodynamic quantities, including freeenergy, entropy, magnetization, susceptibility, and specific heat capacity.Numerical analyses explore how these thermodynamic functions vary with relevantparameters, offering insights into the system's behavior. Additionally, theasymptotic properties of these quantities are examined in the limiting cases\(T \to 0\) and \(T \to \infty\). The findings contribute to a deeperunderstanding of the model's thermodynamic characteristics and highlight itspotential applications across various disciplines.

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