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Comparative study of the critical behavior in one-dimensional random and aperiodic environments

机译:一维随机和非周期性环境中临界行为的比较研究

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We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents ω > 0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as L ~ (lnt)~(1/ω). Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of ω, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities.
机译:我们考虑在一维波动的随机和非周期性环境中的合作过程(量子自旋链和随机游动),这些环境的波动指数ω>0。在临界点,随机和非周期性系统基本上以类似的方式各向异性地扩展:长度(L)时间(t)的尺度与L〜(lnt)〜(1 /ω)相关。还发现一些表征平均数量奇异性的关键指数是ω的通用函数,而其他一些指数确实取决于无序分布的细节。在非关键区域中,两种类型的环境之间存在重要差异:在非周期性系统中,没有额外的(格里菲思)奇点。

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