arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1010.3583cond-mat.soft
收藏

淬火无序流体：临界点附近自由能垒的标度

Fluids with quenched disorder: Scaling of the free energy barrier near critical points

T. Fischer, R. L. C. Vink

备注：
sent to J. Phys. Cond. Matt
发表信息：
2011 J. Phys.: Condens. Matter 23 234117
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

在蒙特卡罗模拟的背景下，如在有限线性扩展$L$的模拟盒中获得的，对序参数$m$的概率分布$P_L(m)$的分析允许容易地估计临界点和临界指数的位置。对于没有淬火无序的类伊辛系统，$P_L(m)$在临界点处变得尺度不变，在临界点处，它呈现具有两个重叠峰的特征双峰形状。特别地，峰值处的$P_L(m)$值（$P_{L, max}$）与中间最小值处的值（$P_{L, min}$）之间的比率在临界状态下变得与$L$无关。然而，对于具有猝灭随机场的类伊辛系统，我们认为应该观察到$ΔF_L := \ln (P_{L, max} / P_{L, min}) \propto L^θ$，其中$θ>0$是“超标度违反”指数。由于$θ$基本上为非零，因此在仿真中应当容易地检测到$ΔF_L$随系统大小的缩放。对于具有淬火无序的两个流体模型，测量了$ΔF_L$与$L$，并且证实了预期的缩放。这进一步证明了具有淬火无序的流体属于无规场伊辛模型的普适类。

英文摘要：

In the context of Monte Carlo simulations, the analysis of the probability distribution $P_L(m)$ of the order parameter $m$, as obtained in simulation boxes of finite linear extension $L$, allows for an easy estimation of the location of the critical point and the critical exponents. For Ising-like systems without quenched disorder, $P_L(m)$ becomes scale invariant at the critical point, where it assumes a characteristic bimodal shape featuring two overlapping peaks. In particular, the ratio between the value of $P_L(m)$ at the peaks ($P_{L, max}$) and the value at the minimum in-between ($P_{L, min}$) becomes $L$-independent at criticality. However, for Ising-like systems with quenched random fields, we argue that instead $ΔF_L := \ln (P_{L, max} / P_{L, min}) \propto L^θ$ should be observed, where $θ>0$ is the "violation of hyperscaling" exponent. Since $θ$ is substantially non-zero, the scaling of $ΔF_L$ with system size should be easily detectable in simulations. For two fluid models with quenched disorder, $ΔF_L$ versus $L$ was measured, and the expected scaling was confirmed. This provides further evidence that fluids with quenched disorder belong to the universality class of the random-field Ising model.

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。

↑