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One-dimensional systems with short-range interactions cannot exhibit along-range order at nonzero temperature. However, there are some particularone-dimensional models, such as the Ising-Heisenberg spin models with a varietyof lattice geometries, which exhibit unexpected behavior similar to thediscontinuous or continuous temperature-driven phase transition. Although thesepseudo-transitions are not true temperature-driven transitions showing onlyabrupt changes or sharp peaks in thermodynamic quantities, they may be confusedwhile interpreting experimental data. Here we consider the spin-$\frac{1}{2}$Ising-XYZ diamond chain in the regime when the model exhibitstemperature-driven pseudo-transitions. We provide a detailed investigation ofseveral correlation functions between distant spins that illustrates theproperties of quasi-phases separated by pseudo-transitions. Inevitably, allcorrelation functions show the evidence of pseudo-transition, which aresupported by the analytical solutions and, besides we provide a rigorousanalytical investigation around the pseudo-critical temperature. It is worth tomention that the correlation functions between distant spins have an extremelylarge correlation length at pseudo-critical temperature.

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