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The q-state Potts model on a diamond chain has mathematical significance inanalyzing phase transitions and critical behaviors in diverse fields, includingstatistical physics, condensed matter physics, and materials science. Byfocusing on the 3-state Potts model on a diamond chain, we reveal rich andanalytically solvable behaviors without phase transitions at finitetemperatures. Upon investigating thermodynamic properties such as internalenergy, entropy, specific heat, and correlation length, we observe sharpchanges near zero temperature. Magnetic properties, including magnetization andmagnetic susceptibility, display distinct behaviors that provide insights intospin configurations in different phases. However, the Potts model lacks genuinephase transitions at finite temperatures, in line with the Peierls argument forone-dimensional systems. Nonetheless, in the general case of an arbitrary$q$-state, magnetic properties such as correlation length, magnetization, andmagnetic susceptibility exhibit intriguing remnants of a zero-temperature phasetransition at finite temperatures. Furthermore, residual entropy uncoversunusual frustrated regions at zero-temperature phase transitions. This featureleads to the peculiar thermodynamic properties of phase boundaries, including asharp entropy change resembling a first-order discontinuity without an entropyjump, and pronounced peaks in second-order derivatives of free energy,suggestive of a second-order phase transition divergence, but withoutsingularities. This unusual behavior is also observed in the correlation lengthat the pseudo-critical temperature, which could potentially be misleading as adivergence.

Zero temperature phase transitions and their anomalous influence on thermodynamic behavior in the q-state Potts model on a diamond chain