J1-J2 Potts模型猝灭动力学中的对数标度校正
Logarithmic scaling correction in quench dynamics of the J1-J2 Potts model
AI总结：
研究J1-J2反铁磁Potts模型在热猝灭下的对数标度校正，通过构建平衡相图设计四个猝灭协议，发现QLRO相终止的猝灭有对数校正KZM标度，LRO相结束的遵循幂律标度，为KZM光子模拟实验提供理论指导。
AI中文摘要：
在由Kibble-Zurek机制（KZM）控制的传统猝灭动力学中，缺陷密度通常作为猝灭速率的纯幂律衰减。然而，具有拓扑相变的二维（2D）XY模型的KZM标度具有显著的对数校正。目前尚不清楚在热猝灭下经历两次连续拓扑相变的离散自旋系统中是否会出现这种对数标度校正。本文研究了J1-J2反铁磁Potts模型并构建了其平衡相图。基于顺磁相、准长程有序（QLRO）相、长程有序相和零温基态的温度范围，设计了四个具有不同温度区间的猝灭协议。结果表明，在QLRO相终止的猝灭表现出对数校正的过剩能量密度的KZM标度，与2D XY模型的动力学普适类一致。相比之下，在LRO相结束的猝灭，包括有限温度和零温度协议，遵循传统的幂律标度。我们的结果清楚地揭示了J1-J2 Potts模型的特征标度校正，并为未来通过光子模拟平台对KZM进行实验研究提供了理论指导。
英文摘要：
In conventional quench dynamics governed by the Kibble-Zurek mechanism (KZM), the defect density generally decays as a pure power law of the quench rate. However, the KZM scaling of the two-dimensional (2D) XY model with topological phase transitions features prominent logarithmic corrections. Nevertheless, it remains unclear whether such logarithmic scaling corrections emerge in discrete-spin systems that host two successive topological phase transitions under thermal quenches. This work investigates the J1-J2 antiferromagnetic Potts model and constructs its equilibrium phase diagram. Based on the temperature ranges of the paramagnetic phase, quasi-long-range ordered (QLRO) phase, long-range ordered phase, and zero-temperature ground state, we design four quench protocols with distinct temperature intervals. Our results demonstrate that quenches terminating in the QLRO phase exhibit logarithmically corrected KZM scaling of the excess energy density, consistent with the dynamical universality class of the 2D XY model. In contrast, quenches ending in the LRO phase, including both finite-temperature and zero-temperature protocols, follow conventional power-law scaling. Our results clearly uncover the characteristic scaling corrections of the J1-J2 Potts model and offer theoretical guidance for future experimental investigations of KZM via photonic simulation platforms.
