Duarte Queirós Sílvio M, Crokidakis Nuno, Soares-Pinto Diogo O
Unilever R&D Port Sunlight, Quarry Road East, Wirral CH63 3JW, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 1):011143. doi: 10.1103/PhysRevE.80.011143. Epub 2009 Jul 30.
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).
在无限范围相互作用的极限情况下，研究了局部磁场概率密度函数（PDF）的尾部特征对铁磁伊辛模型的影响。具体而言，我们给每个格点赋予一个淬火随机场，其值符合一种通用分布，该分布根据单个参数(\tau\lt3)呈现出低峰态和尖峰态分布。对于(\tau\lt5/3)，这些基本上是为所有合理实自由度扩展的学生(t)分布和(r)分布，具有有限标准差，否则该分布具有与(\alpha)稳定的列维分布相同的渐近幂律行为，其中(\alpha=(3 - \tau)/(\tau - 1))。对于每个(\tau)值，在特定温度和分布宽度下，系统会经历连续相变。引人注目的是，对于比柯西 - 洛伦兹分布（(\tau = 2)）更宽的分布，我们在温度 - PDF宽度相图中发现了一个拐点的出现，这伴随着每个自旋的自由能发散（在零温度下）。
