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 with 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.

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一维模型临界剩余熵与有限温度伪跃迁关系的猜想

最近在一维自旋模型中观察到伪临界温度线索，例如 Ising-Heisenberg 自旋模型等。在这里，我们报告了零温度相界残余熵（临界残余熵）和伪转变之间的关系。通常，残余熵在相界处增加，这意味着系统与其相邻状态相比在相界处变得更加简并。然而，这并非总是如此; 在零温度下，存在一些相边界，其中熵保持相邻状态的最大残余熵。因此，我们可以提出以下猜想：如果零温下的残余熵是一个连续函数，至少从临界点的单边极限来看，那么在临界点附近的有限温度下会出现伪跃迁证据。我们预计这一论点将适用于研究更现实的模型。只有通过分析零温度下的残余熵，才能先验地确定系统是否会在有限温度下表现出伪跃迁。为了加强我们的猜想，我们使用了两个 Ising-Heisenberg 模型的例子，它们表现出伪过渡行为：一个受挫的耦合四面体链和另一个不受挫的菱形链。