Correlation functions for a spin-12 Ising-XYZ diamond chain: Further evidence for quasi-phases and pseudo-transitions

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-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.σ i+r−1 Figure 1: Schematic representation of spin-1 2 Ising-XYZ diamond chain.

A Conjecture on the Relationship Between Critical Residual Entropy and Finite Temperature Pseudo-transitions of One-dimensional Models

“…For more detailed information concerning Heisenberg spin magnetization, we refer the readers to ref. [10]. In a similar way Fig.…”

“…As discussed previously in refs. [10,12], the pseudo-critical temperature can be found using the following relation…”

“…On the other hand, the term "pseudo-transition" was introduced by Timonin [9] in 2011 while studying the spin ice in a field, and refers to a sudden change in the first derivative of free energy, whereas a strong vigorous peak appears in the second derivative of free energy, although there are no discontinuity or divergence, respectively. Later this definition was adopted for our group [10][11][12] because we found the same kind of property. The pseudo-transition does not violate the Perron-Frobenius theorem [8], since the free energy is always analytic.…”

“…Therefore, this peculiar behavior drew attention to a more careful study, as considered in reference [12]. Lately, in reference [10] has been made an additional discussion on this property and detailed study of the correlation function for arbitrarily distant spins around the pseudo-transition.…”

Universality and quasicritical exponents of one-dimensional models displaying a quasitransition at finite temperatures

“…A further investigation of quasitransitions and quasiphases of one-dimensional spin systems was considered in Ref. [15], where the correlation function around the quasitransition temperature was discussed. The origin of quasitransition is however still not fully understood yet.…”