Unconventional low temperature features in the one-dimensional frustrated $q$-state Potts model

TL;DR

This paper investigates an unusual low-temperature behavior in a one-dimensional q-state Potts model with external field and anisotropic interactions, revealing pseudo-critical phenomena with sharp peaks mimicking phase transitions without true singularities.

Contribution

It uncovers and characterizes anomalous low-temperature features and pseudo-critical behavior in a one-dimensional frustrated Potts model, including analysis of critical exponents and universality classes.

Findings

Entropy shows steep but continuous change at pseudo-critical temperature

Correlation length exhibits a sharp peak similar to divergence

Pseudo-critical exponents match known universality class values

Abstract

Here we consider a one-dimensional $q$-state Potts model with an external magnetic field and an anisotropic interaction that selects neighboring sites that are in the spin state 1. The present model exhibits an unusual behavior in the low-temperature region, where we observe an anomalous vigorous change in the entropy for a given temperature. There is a steep behavior at a given temperature in entropy as a function of temperature, quite similar to first-order discontinuity, but there is no jump in the entropy. Similarly, second derivative quantities like specific heat and magnetic susceptibility also exhibit a strong acute peak rather similar to second-order phase transition divergence, but once again there is no singularity at this point. Correlation length also confirms this anomalous behavior at the same given temperature, showing a strong and sharp peak which easily one may confuse with a divergence. The temperature where occurs this anomalous feature we call pseudo-critical temperature. We have analyzed physical quantities, like correlation length, entropy, magnetization, specific heat, magnetic susceptibility, and distant pair correlation functions. Furthermore, we analyze the pseudo-critical exponent that satisfy a class of universality previously identified in the literature for other one-dimensional models, these pseudo-critical exponents are: for correlation length $\nu=1$, specific heat $\alpha=3$ and magnetic susceptibility $\mu=3$.