一维对生成与三生成过程中的不连续相变
Discontinuous phase transitions in the one-dimensional pair and triplet creation processes
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中文总结 AI 辅助
本文针对迪克曼等人提出的一维对生成与三生成过程模型，严格证明了两类模型在搅拌速率较大时均存在不连续相变，解决了此前关于三生成模型相变类型的争议。
中文摘要 AI 辅助
迪克曼和托梅（1991）在整数集Z上引入了一类模型，其中k个连续被占据的位点以速率λ产生新粒子，单个粒子以速率1死亡，且构型受最近邻搅拌作用。他们声称对生成模型（k=2）具有连续相变，属于定向渗流的普适类；而三生成模型（k=3）在搅拌速率较大时具有不连续（或一阶）相变。欣里希森（2000a）对后一结论提出质疑，认为1+1维非平衡系统中，存在涨落有序相的一阶相变不可能存在。本文严格证明，当搅拌速率较大时，对生成模型与三生成模型的相变均为不连续相变。
英文摘要
Dickman and Tomé (1991) introduced models on $Z$ in which $k$ consecutive occupied sites give birth at rate $λ$, individual particles die at rate 1, and the configuration is subject to nearest neighbor stirring. They claimed that the pair creation model ($k=2$) has a continuous phase transition and was in the universality class of directed percolation, but the triplet creation model ($k=3$) has a discontinuous (or first-order) phase transition when the stirring rate is large. Hinrichsen (2000a) disputed the second claim and argued that first-order phase transitions in 1+1-dimensional nonequilibrium systems with fluctuating ordered phases are impossible. In this paper we prove rigorously that the phase transitions are discontinuous in both the pair and triplet models when the stirring rate is large. At the end of Section 2 we state some open problems and suggest reasons that the results in the physics literature differ from those presented here,
发表机构
- James B. Duke Emeritus Professor of Math（詹姆斯·B·杜克数学荣休教授）
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