Aperiodic and correlated disorder in XY chains: exact results
Aperiodic and correlated disorder in XY chains: exact results
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XY 链中的非周期性和相关无序：精确结果
DOI：
10.1088/0305-4470/33/1/304
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
J. Hermisson
中科院分区：
文献类型：
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作者：
J. Hermisson
我们研究了具有任意取代序列的耦合常数的XY量子链的热力学性质、表面磁化强度、比热和磁化率。推广的精确重整化群（RG）变换，最初制定的伊辛量子链，我们得到了这类模型的Harris-Luck型的精确相关准则。对于两个字母的替代规则，给出了一个详细的分类序列导致无关，边际或相关的非周期性调制。我们发现，在一般情况下，相同的非周期耦合序列的相关性将是不同的XY和伊辛量子链。通过我们的方法，连续变化的临界指数可以精确地计算任意（两个字母）的替代规则与边际非周期性。给出了一些例子，包括倍周期链、三重链和精确平均链。我们还讨论了扩展的重正化方法的一类特殊的长程相关随机链，产生的随机替换。
We study thermodynamic properties, surface magnetization, specific heat and susceptibility of XY quantum chains with coupling constants following arbitrary substitution sequences. Generalizing an exact renormalization group (RG) transformation, originally formulated for Ising quantum chains, we obtain exact relevance criteria of Harris-Luck-type for this class of models. For two-letter substitution rules, a detailed classification is given of sequences leading to irrelevant, marginal or relevant aperiodic modulations. We find that the relevance of the same aperiodic sequence of couplings in general will be different for XY and Ising quantum chains. By our method, continuously varying critical exponents may be calculated exactly for arbitrary (two-letter) substitution rules with marginal aperiodicity. A number of examples are given, including the period-doubling, three-folding and precious mean chains. We also discuss extensions of the renormalization approach to a special class of long-range correlated random chains, generated by random substitutions.