二维Ising铁磁体损伤扩展与损伤愈合的Monte Carlo研究
A Model for Damage Spreading with Damage Healing: Monte Carlo Study of the two Dimensional Ising Ferromagnet
摘要：
本文提出了一种具有损伤愈合概率的损伤扩展伊辛模型（$q = 1 - p$），并通过Monte Carlo模拟对该模型进行了研究。在极限$p \to 1$中，新模型被映射到标准伊辛模型。研究发现，当温度高于Onsager临界温度（$T_{C}$）时，存在一个非平凡的$p$有限值，它决定了损伤扩展的临界点（$p_{c}$）.发现$p_{c}$依赖于$T$，在损伤扩展和损伤愈合的边界处定义了一条临界曲线。沿这条曲线的相变属于定向渗流的普适类。该模型的相图也进行了评估，显示出大$T$一个有$p_{c} \propto (T- T_{C})^α$，与$α= 1$。在损伤保持活跃的阶段内，损伤的稳态值线性地取决于$p - p_{c}$和$T - T_{C} $。
英文摘要：
An Ising model for damage spreading with a probability of damage healing ($q = 1 - p$) is proposed and studied by means of Monte Carlo simulations. In the limit $p \to 1$ the new model is mapped to the standard Ising model. It is found that, for temperatures above the Onsager critical temperature ($T_{C}$), there exist a no trivial finite value of $p$ that sets the critical point ($p_{c}$) for the onset of damage spreading. It is found that $p_{c}$ depends on $T$, defining a critical curve at the border between damage spreading and damage healing. Transitions along such curve are found to belong to the universality class of directed percolation. The phase diagram of the model is also evaluated showing that for large $T$ one has $p_{c} \propto (T- T_{C})^α$, with $α= 1$. Within the phase where the damage remains active, the stationary value of the damage depends lineally on both $p - p_{c}$ and $T - T_{C} $.
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。
