面心立方格子上Ising自旋Ⅰ(1)的反铁磁性——配分函数的级数展开法

本文采用与文献[1]完全相类似的方法作出一般化Ising模型s=1在面心立方格子(fcc)上最近邻相互作用的反铁磁系统的统计理论,即用Pad近似式处理配分函数的高、低温幂级数有限项展开式,得出其反铁磁-顺磁转变为一阶相变。T_c=1.33J/k,小于(1/2)相应的相变点。文中算出了相关的热力学量如内能、潜热、熵、比热、长程和短程序参量,以及磁化率等。值得指出的是:(1)fcc上反铁磁-顺磁相变属于一阶,这是由格子密堆积的拓扑特征所决定,与s的大小无关;(2)T_c(s)随s的增加而缓慢地下降。关键词：

STATISTICAL THEORY OF I(1) MODEL ANTIFERROMAGNE-TISM ON A FACE CENTERED CUBIC LATTICE WITH NEAREST-NEIGHBOR INTERACTION——A SERIES EXPANSION METHOD

The antiferromagnetism of Ising spin I(1) with the nearest neighbor interaction -J on fcc has been treated by the method of series expansion similar to [1]. The free energy function for the lower temperature ordered state is written in a series of exp(-J/kT) and that for the higher temperature disorder state in a series of J/kT. Using the Padé approximants we have shown clearly that the free energy curves of the two states cross at T_c= 1.33 J/k. The transition is one of the first order, the same conclusion as we obtained for the I(1/2) model, but T_c of I(1) is lower than that of I(1/2). The thermodynamic quantities such as the long-range and short-range order parameter, the internal energy, the entropy, the specific heat as well as the magnetic susceptibility were calculated in variation with temperature. They all change abruptly at T_c.We concluded that (1) on fcc the Ising spin AM-PM transtion being one of the first order should be attributed to the close-packing characteristics of this lattice; and (2) T_c(s) decreases as s increases.