随机场伊辛模型中板状和尖峰分布的影响：平均场方法
Effect of platy- and leptokurtic distributions in the random-field Ising model: Mean field approach
摘要：
在无限程相互作用的极限下，研究了局域磁场概率密度函数尾部特征对铁磁伊辛模型的影响.具体来说，我们分配一个淬火随机场，其值是根据一个通用的分布，承担platykurtic和leptokurtic分布取决于一个单一的参数$τ< 3$到每个网站。对于$τ< 5/3$，这种分布基本上是Student- $t$和$r$ -分布，扩展到所有合理的实自由度，呈现有限的标准差，如果不是，则该分布具有与具有$α= (3 - τ)/(τ- 1)$的$α$ -稳定Lévy分布相同的渐近幂律行为。对于每个$τ$值，在特定的温度和分布宽度下，系统经历连续相变。引人注目的是，我们传授的温度-PDF宽度相图中出现的一个cubon点的分布比柯西-洛伦兹（$τ= 2$），这是伴随着发散的自由能每自旋（在零温度）。
英文摘要：
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 $τ< 3$ to each site. For $τ< 5/3$, 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 $α$-stable Lévy distribution with $α= (3 - τ)/(τ- 1)$. For every value of $τ$, 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 ($τ= 2$) which is accompanied with a divergent free energy per spin (at zero temperature).
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