Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model
Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model
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磁场中的自由能和三维伊辛模型的通用标度状态方程
DOI：
10.1103/physrevb.83.054433
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发表时间：
2010
影响因子：
3.7
通讯作者：
M. Pernici
中科院分区：
文献类型：
--
作者：
P. Butera;M. Pernici
对于传统的三维伊辛模型和一般假定属于同一临界普适类的各种其他自旋系统，我们已经充分地扩展了自由能的高温和低磁场（以及相关的低温和高磁场）二元展开式。特别地，我们还导出了自旋为s= 1，3/2，\dots {}$的伊辛模型和具有四次自相互作用的格点欧几里德标量场理论在单立方和体心立方格点上的类似展开式。我们的二元高温膨胀，延伸到第24阶，使我们能够计算，通过相同的顺序，所有更高的衍生物的自由能相对于该领域，即所有更高的磁化率。这些数据使更准确的检查可能，在临界条件下，无论是缩放和普遍性属性相对于晶格和相互作用结构，也有助于提高近似参数表示的临界状态方程的三维伊辛模型的普遍性类。
We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a variety of other spin systems generally assumed to belong to the same critical universality class. In particular, we have also derived the analogous expansions for the Ising models with spin $s=1,3/2,\dots{}$ and for the lattice Euclidean scalar-field theory with quartic self-interaction, on the simple-cubic and the body-centered-cubic lattices. Our bivariate high-temperature expansions, which extend through 24th order, enable us to compute, through the same order, all higher derivatives of the free energy with respect to the field, namely, all higher susceptibilities. These data make more accurate checks possible, in critical conditions, both of the scaling and the universality properties with respect to the lattice and the interaction structure and also help to improve an approximate parametric representation of the critical equation of state for the three-dimensional Ising model universality class.