三维经典海森堡模型中表面特殊转变的有限时间标度
Finite-time Scaling of the surface special transition in a 3D classical Heisenberg model
浏览论文内容
中文总结 AI 辅助
研究三维经典海森堡模型表面特殊相变的非平衡驱动动力学，用蒙特卡罗模拟实现多种驱动协议。发现从非凡对数临界态驱动时大速率标度关系有对数修正，通过对数初始态记忆证明源于有限时间标度框架，扩展了边界有限时间标度。
中文摘要 AI 辅助
我们研究了具有开放边界的三维经典海森堡模型中跨越特殊表面相变的非平衡驱动动力学，通过调整表面耦合可进入一个具有非凡对数边界临界态，其关联呈对数而非幂律衰减。利用蒙特卡罗模拟实现了四种驱动协议。对于温度驱动协议，表面序参量遵循有限时间标度和基布尔 - 祖雷克机制的推广。从非凡对数临界态驱动系统时，大速率标度关系有对数修正，呈现新形式。通过纳入对数初始态记忆证明此形式源于一般有限时间标度框架，并在广泛系统尺寸和驱动速率范围内实现了良好的数据塌缩。结果表明非凡对数初始态改变非平衡临界标度，扩展了边界有限时间标度。
英文摘要
We investigate nonequilibrium driven dynamics across the special surface phase transition in the three-dimensional classical Heisenberg model with open boundaries, where tuning the surface coupling gives access to an extraordinary-log boundary critical state characterized by logarithmic, rather than power-law, decay of correlations. Using Monte Carlo simulations, we realize four driving protocols: temperature heating and cooling across the special transition, and surface-coupling ramps from the ordinary and extraordinary-log critical states into the special point. For temperature-driven protocols, the surface order parameter obeys a generalization of the finite-time scaling (FTS) and the Kibble-Zurek mechanism. The central finding emerges when the system is driven from the extraordinary-log critical state: the large-rate scaling relation acquires a logarithmic correction and takes the novel form $M^{2}_{s}\propto R^{(1+η_{s})/r_{s}}[\log(LR^{1/η_{s}})]^{-q}$ , where $R$ is the driving rate, $L$ the system size, $η_{s}$ the surface anomalous dimension, $r_{s}$ the scaling dimension of $R$, and $q$ the exponent governing the logarithmic boundary criticality. We demonstrate that this form follows from the general FTS framework by incorporating the logarithmic initial-state memory, and we achieve excellent data collapse over a wide range of system sizes and driving rates. Our results establish that extraordinary-log initial states alter nonequilibrium critical scaling, extending boundary FTS beyond conventional power-law initial conditions.
