Correlation functions for a spin-$\frac{1}{2}$ Ising-XYZ diamond chain: Further evidence for quasi-phases and pseudo-transitions

TL;DR

This paper investigates the behavior of correlation functions in a spin-1/2 Ising-XYZ diamond chain, revealing pseudo-transitions and quasi-phases characterized by large correlation lengths, supported by analytical solutions.

Contribution

It provides a detailed analytical study of correlation functions around pseudo-critical temperatures in a specific one-dimensional quantum spin model.

Findings

Correlation functions exhibit pseudo-transition signatures.

Distant spin correlations show extremely large correlation lengths.

Analytical solutions confirm pseudo-critical behavior.

Abstract

One-dimensional systems with short-range interactions cannot exhibit a long-range order at nonzero temperature. However, there are some particular one-dimensional models, such as the Ising-Heisenberg spin models with a variety of lattice geometries, which exhibit unexpected behavior similar to the discontinuous or continuous temperature-driven phase transition. Although these pseudo-transitions are not true temperature-driven transitions showing only abrupt changes or sharp peaks in thermodynamic quantities, they may be confused while interpreting experimental data. Here we consider the spin-$\frac{1}{2}$ Ising-XYZ diamond chain in the regime when the model exhibits temperature-driven pseudo-transitions. We provide a detailed investigation of several correlation functions between distant spins that illustrates the properties of quasi-phases separated by pseudo-transitions. Inevitably, all correlation functions show the evidence of pseudo-transition, which are supported by the analytical solutions and, besides we provide a rigorous analytical investigation around the pseudo-critical temperature. It is worth to mention that the correlation functions between distant spins have an extremely large correlation length at pseudo-critical temperature.