XX0自旋链的相结构与非相交布朗运动
Phase Structure of XX0 Spin Chain and Nonintersecting Brownian Motion
摘要：
本文研究了有限尺寸和有限温度的XX 0海森堡自旋链在弱耦合和强耦合两种情况下的性质。通过使用一个优雅的连接的模型，可积组合数学和概率，我们探索和解释一个可能的相结构的模型在渐近极限：大逆温度和尺寸的限制。首先，利用随机矩阵模型和不相交布朗运动的技巧和结果，导出了模型的配分函数和自由能。我们表明，在渐近极限，配分函数的模型，写在矩阵积分，是由Tracy-Widom分布。第二，通过对Tracy-Widom分布的渐近分析得到的自由能的精确解析结果表明了该模型的一种全新的复杂的相结构。该相结构由二阶和三阶相变组成。最后，为了阐明我们的新结果，我们提供了一个可能的解释相结构的自旋链中的磁振子的动力学行为。我们展示了不同的功能的相位与示意性的自旋配置有明确的功能，在相图的每个区域。
英文摘要：
We study finite size and temperature XX0 Heisenberg spin chain in weak and strong coupling regimes. By using an elegant connection of the model to integrable combinatorics and probability, we explore and interpret a possible phase structure of the model in asymptotic limit: the limit of large inverse temperature and size. First, partition function and free energy of the model are derived by using techniques and results from random matrix models and nonintersecting Brownian motion. We show that, in the asymptotic limit, partition function of the model, written in terms of matrix integral, is governed by the Tracy-Widom distribution. Second, the exact analytic results for the free energy, which is obtained by the asymptotic analysis of the Tracy-Widom distribution, indicate a completely new and sophisticated phase structure of the model. This phase structure consists of second- and third-order phase transitions. Finally, to shed light on our new results, we provide a possible interpretation of the phase structure in terms of dynamical behavior of magnons in the spin chain. We demonstrate distinct features of the phases with schematic spin configurations which have definite features in each region of the phase diagram.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
