EN
首页 资讯 期刊 导师 问答 求职 发Paper 文献直达 高级搜索 期刊列表
当前位置： X-MOL 学术 › Phys. Rev. E › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Universal function of the nonequilibrium phase transition of a nonlinear Pólya urn
Physical Review E ( IF 2.2 ) Pub Date : 2021-07-12 , DOI: 10.1103/physreve.104.014109
Kazuaki Nakayama 1 , Shintaro Mori 2
Affiliation  

We study the phase transition and the critical properties of a nonlinear Pólya urn, which is a simple binary stochastic process X(t)∈{0,1},t=1,⋯, with a feedback mechanism. Let f be a continuous function from the unit interval to itself, and z(t) be the proportion of the first t variables X(1),⋯,X(t) that take the value 1. X(t+1) takes the value 1 with probability f[z(t)]. When the number of stable fixed points of f(z) changes, the system undergoes a nonequilibrium phase transition and the order parameter is the limit value of the autocorrelation function. When the system is Z2 symmetric, that is, f(z)=1−f(1−z), a continuous phase transition occurs, and the autocorrelation function behaves asymptotically as ln(t+1)−1/2g[ln(t+1)/ξ], with a suitable definition of the correlation length ξ and the universal function g(x). We derive g(x) analytically using stochastic differential equations and the expansion about the strength of stochastic noise. g(x) determines the asymptotic behavior of the autocorrelation function near the critical point and the universality class of the phase transition.

中文翻译：
非线性 Pólya 瓮的非平衡相变的通用函数

我们研究非线性 Pólya 瓮的相变和临界性质，这是一个简单的二元随机过程 十(吨)∈{0,1},吨=1,⋯，有反馈机制。让f 是从单位区间到自身的连续函数，并且 z(吨) 成为第一的比例 吨 变量 十(1),⋯,十(吨) 取值为 1。 十(吨+1) 以概率取值 1 f[z(吨)]. 当稳定不动点数为f(z)变化，系统发生非平衡相变，阶次参数为自相关函数的极限值。当系统是Z2 对称，即 f(z)=1-f(1-z)，发生连续相变，自相关函数渐近表现为 输入(吨+1)-1/2克[输入(吨+1)/ξ], 相关长度的合适定义 ξ 和通用功能 克(×). 我们推导出克(×) 分析使用随机微分方程和关于随机噪声强度的扩展。 克(×) 确定临界点附近自相关函数的渐近行为和相变的普遍性类。
更新日期：2021-07-12
  点击分享   查看原文
点击收藏
阅读更多本刊最新论文 本刊介绍/投稿指南11
down
wechat
bug