Effect of platykurtic and leptokurtic distributions in the random-field Ising model: mean-field approach.
Effect of platykurtic and leptokurtic distributions in the random-field Ising model: mean-field approach.
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DOI：
10.1103/physreve.80.011143
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发表时间：
2009-06
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影响因子：
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通讯作者：
S. M. Duarte Queirós;N. Crokidakis;Diogo O. Soares-Pinto
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文献类型：
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作者：
S. M. Duarte Queirós;N. Crokidakis;Diogo O. Soares-Pinto
在无限距离相互作用的极限下，研究了局部磁场概率密度函数（PDF）的尾部特征对铁磁Ising模型的影响。具体来说，我们为每个位点分配了一个淬灭随机场，该随机场的值符合一般分布，根据单个参数tau<3，该分布具有平峰分布和细峰分布。对于tau<5/3，这些分布基本上是对所有可能的实自由度进行扩展的Student-t和r分布，呈现有限的标准差，如果不是，则该分布具有与α =(3-tau)/(tau-1)的α -稳定lsamvy分布相同的渐近幂律行为。对于每一个tau值，在特定的温度和分布宽度下，系统经历一个连续的相变。引人注目的是，我们在比柯西-洛伦兹（tau=2）更宽的分布的温度- pdf宽度相图中发现了一个拐点，该拐点伴随着每自旋的发散自由能（在零温度下）。
The influence of the tail features of the local magnetic field probability density function (PDF) on the ferromagnetic Ising model is studied in the limit of infinite range interactions. Specifically, we assign a quenched random field whose value is in accordance with a generic distribution that bears platykurtic and leptokurtic distributions depending on a single parameter tau<3 to each site. For tau<5/3, such distributions, which are basically Student-t and r distribution extended for all plausible real degrees of freedom, present a finite standard deviation, if not the distribution has got the same asymptotic power-law behavior as a alpha-stable Lévy distribution with alpha=(3-tau)/(tau-1). For every value of tau, at specific temperature and width of the distribution, the system undergoes a continuous phase transition. Strikingly, we impart the emergence of an inflexion point in the temperature-PDF width phase diagrams for distributions broader than the Cauchy-Lorentz (tau=2) which is accompanied with a divergent free energy per spin (at zero temperature).