A conjecture on the relationship between critical residual entropy and finite temperature pseudo-transitions of one-dimensional models

TL;DR

This paper proposes a conjecture linking zero-temperature residual entropy to the occurrence of pseudo-transitions at finite temperature in one-dimensional spin models, supported by analysis of specific Ising-Heisenberg models.

Contribution

It introduces a new conjecture connecting critical residual entropy with pseudo-transitions, providing a method to predict finite-temperature behavior from zero-temperature entropy analysis.

Findings

Residual entropy at phase boundaries can be maximal or not, affecting pseudo-transition occurrence.

The conjecture is supported by analysis of two Ising-Heisenberg models with pseudo-transition behavior.

Zero-temperature residual entropy analysis can predict pseudo-transitions in realistic models.

Abstract

Recently pseudo-critical temperature clues were observed in one-dimensional spin models, such as the Ising-Heisenberg spin models, among others. Here we report a relationship between the zero-temperature phase boundary residual entropy (critical residual entropy) and pseudo-transition. Usually, the residual entropy increases in the phase boundary, which means the system becomes more degenerate at the phase boundary compared to its adjacent states. However, this is not always the case; at zero temperature, there are some phase boundaries where the entropy holds the largest residual entropy of the adjacent states. Therefore, we can propose the following conjecture: If residual entropy at zero-temperature is a continuous function at least from the one-sided limit at a critical point, then pseudo-transition evidence will appear at finite temperature near the critical point. We expect that this argument would apply to study more realistic models. Only by analyzing the residual entropy at zero temperature, one could identify a priori whether the system will exhibit the pseudo-transition at finite temperature. To strengthen our conjecture, we use two examples of Ising-Heisenberg models, which exhibit pseudo-transition behavior: one frustrated coupled tetrahedral chain and another unfrustrated diamond chain.