[论文解读] Frustration-driven unconventional phase transitions at finite temperature in a one-dimensional ladder Ising model

Wei‐Guo Yin|arXiv (Cornell University)|Jun 16, 2020

Quantum many-body systems参考文献 11被引用 4

一句话总结

该论文展示了在一维两腿 ladder Ising 模型中存在有限温度相变，该模型具有强烈的几何阻挫，打破了传统一维系统无相变定理。尽管阻挫强烈，系统仍表现出尖锐的比热峰、大的潜热以及非传统的序参量，揭示了熵驱动的中间有序相，并在高温区出现一种非平均场方式抑制腿间耦合的解耦奇异正常态。

ABSTRACT

The Ising model, with short-range interactions between constituents, is a basic mathematical model in statistical mechanics. It has been widely used to describe collective phenomena such as order-disorder phase transitions in various physical, biological, economical, and social systems. However, it was proven that spontaneous phase transitions do not exist in the one-dimensional Ising models. Besides low dimensionality, frustration is the other well-known suppressor of phase transitions. Here I show that surprisingly, a strongly frustrated one-dimensional two-leg ladder Ising model can exhibit a marginal finite-temperature phase transition. It features a large latent heat, a sharp peak in specific heat, and unconventional order parameters, which classify the transition as involving an entropy-favored intermediate-temperature ordered and further unveil a crossover to an exotic normal state in which frustration effectively decouples the two strongly interacted legs in a counterintuitive non-mean-field way. These exact results expose a mathematical structure that has not appeared before in phase-transition problems, and shed new light on our understanding of phase transitions and the dynamical actions of frustration. Applications of this model and its mechanisms to various systems with extensions to consider higher dimensions, quantum characters, or external fields, etc. are anticipated and briefly discussed---with insights into the puzzling phenomena of strange strong frustration and intermediate-temperature orders such as the Bozin-Billinge orbital-degeneracy-lifting recently discovered in real materials.

研究动机与目标

• 研究强阻挫是否能在一维 Ising 系统中诱导有限温度相变，与既有的无相变定理相悖。
• 确定所涌现有序相的本质以及熵在强阻挫下稳定该相的作用。
• 揭示阻挫如何导致高温相中两腿的非平均场解耦机制。
• 探讨该非传统相变对理解真实材料中中间温度有序与强阻挫的启示。

提出的方法

• 精确解析求解具有腿上铁磁相互作用与横档反铁磁相互作用竞争的两腿 Ising ladder 模型，引入几何阻挫。
• 使用转移矩阵方法计算比热、自由能等热力学量随温度的变化。
• 引入非传统序参量以分类不同相态，包括中间有序态。
• 分析从有序相到高温奇异正常态的交叉行为，该态中腿间关联虽强但已消失。
• 识别出大的潜热与尖锐的比热峰，作为一级相变样行为的标志。
• 对底层数学结构进行分析，揭示相变理论中此前未见的机制。

实验结果

研究问题

• RQ1 在一维 Ising 模型中，即使标准一维模型中不存在自发长程序，强阻挫是否仍能导致有限温度相变？
• RQ2 在强阻挫下，由熵稳定存在的中间温度有序相的本质是什么？
• RQ3 阻挫如何导致高温相中两腿的非平均场解耦？
• RQ4 非传统序参量在表征相变与区分各相中起什么作用？
• RQ5 该机制如何解释如 Bozin-Billinge 轨道简并性消除等真实材料中出现的中间温度有序与强阻挫等谜题现象？

主要发现

• 该模型表现出有限温度相变，比热出现尖锐峰值并伴随大的潜热，表明尽管存在一维约束，仍呈现一级相变样行为。
• 熵驱动的中间温度有序相出现，其稳定性源于熵效应而非能量偏好。
• 该相变由非传统序参量分类，可将有序相与高温态区分开。
• 在高温相中，阻挫以非平均场方式有效解耦两腿，形成一种新颖的奇异正常态。
• 系统表现出向一种状态的交叉转变，尽管耦合较强，但腿间关联已消失，这是由于阻挫诱导的屏蔽效应。
• 该相变背后的数学结构在相变理论中前所未有，提示了理解低维系统中阻挫的新路径。