损伤扩散与损伤愈合模型的Monte Carlo研究 二维Ising铁磁体

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摘要翻译：
提出了一个具有损伤愈合概率($q=1-p$)的损伤扩散Ising模型，并用Monte Carlo模拟方法进行了研究。在$P\到1$的范围内，新模型映射到标准伊辛模型。研究发现，对于高于Onsager临界温度($t_{C}$)的温度，存在一个有限值$p$，它确定了损伤扩展的临界点($p_{C}$)。发现$P_{c}$依赖于$T$,定义了损伤扩散和损伤愈合边界处的临界曲线。沿这条曲线的跃迁属于有向渗流的普遍性范畴。计算了模型的相图，结果表明，对于较大的$T$1，有$P_{c}\propto(T-T_{c}）^{\alpha}$，$\alpha=1$。在伤害保持活动的阶段内，伤害的固定值与$p-p_{c}$和$t-t_{c}$成线性关系。
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英文标题：
《A Model for Damage Spreading with Damage Healing: Monte Carlo Study of
  the two Dimensional Ising Ferromagnet》
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作者：
M. Leticia Rubio Puzzo and Ezequiel V. Albano
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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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 $p_{c} \propto (T- T_{C})^{\alpha}$, with $\alpha = 1$. 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} $.
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PDF链接：
https://arxiv.org/pdf/705.4466

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关键词：Monte Carlo Carlo mont isi ING healing found 研究 critical 标准