论文标题
带有随机重置的模型
Ising model with stochastic resetting
论文作者
论文摘要
我们研究了Ising模型的固定特性，尽管Glauber Dynamics在温度下向其在温度下朝着其平衡状态发展，但随机重置其固定的初始配置，并以磁化$ m_0 $以恒定的速率$ r $ $ $ $ $ $ $ $ $ $ $ $。重置打破详细的平衡，并将系统驱动到非平衡的固定状态，在该状态下，磁力化获得了非平凡的分布，从而导致$（t，r）$平面的丰富相图。我们在二维中支持的一维和当前缩放参数中精确地建立了这些结果。我们表明，重置产生了$ r> r> r> r^*（t）$和$ t> t_c $的$（t，r）$平面中的小说“伪 - 弗罗”阶段，其中$ r^*（t）$是分隔伪佛罗级阶段的交叉线。该伪 - 弗罗相的特征是非零典型磁化和接近磁化分布的$ m = 0 $的消失间隙。
We study the stationary properties of the Ising model that, while evolving towards its equilibrium state at temperature $T$ according to the Glauber dynamics, is stochastically reset to its fixed initial configuration with magnetisation $m_0$ at a constant rate $r$. Resetting breaks detailed balance and drives the system to a non-equilibrium stationary state where the magnetisation acquires a nontrivial distribution, leading to a rich phase diagram in the $(T,r)$ plane. We establish these results exactly in one-dimension and present scaling arguments supported by numerical simulations in two-dimensions. We show that resetting gives rise to a novel "pseudo-ferro" phase in the $(T,r)$ plane for $r > r^*(T)$ and $T>T_c$ where $r^*(T)$ is a crossover line separating the pseudo-ferro phase from a paramagnetic phase. This pseudo-ferro phase is characterised by a non-zero typical magnetisation and a vanishing gap near $m=0$ of the magnetisation distribution.
