Numerical studies of the Ising chain with long-range ferromagnetic interactions
Numerical studies of the Ising chain with long-range ferromagnetic interactions
复制标题
具有长程铁磁相互作用的伊辛链的数值研究
DOI：
10.1088/0022-3719/3/2/017
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发表时间：
1970
期刊：
影响因子：
--
通讯作者：
J. Bonner
中科院分区：
文献类型：
--
作者：
J. Nagle;J. Bonner
通过对N自旋序列的热力学性质的精确数值计算，研究了具有铁磁性1/R3型相互作用的长程伊辛链。通过将序列用级数表示，并使用Pade近似等外推方法，作者找到了一种一致的方法来获得临界温度，对于甚长程等效邻模型，其精度可达0.4%。作者估算了无限链的高温磁化率和低温长程关联，并由此估算了临界指数γ和β。虽然相变的性质对于1或约为1.3时似乎是经典的，但对于1.6时S而言肯定不是经典的；特别是当S从下方接近2时，伽马有规律地增加到约2或更大，而贝塔有规律地减小到接近0。
A long-range Ising chain, which has ferromagnetic 1/r3 type interactions, has been studied by exact numerical calculation of thermodynamic properties of the sequence of systems of N spins (N<or=30). By expressing the sequence in terms of a series and using extrapolation methods such as the Pade approximant, the authors have found a consistent way to obtain critical temperatures which is accurate to 0.4% for the very long-range equivalent neighbour model. The authors have estimated the high-temperature susceptibility and the low- temperature long-range correlations of the infinite chain and thence have made estimates for the critical exponents gamma and beta . Although the nature of the phase transition appears to be classical for 1<s<or approximately=1.3, it is certainly not classical for 1.6<s<2; in particular, as s approaches 2 from below, gamma increases regularly to about 2 or greater and beta decreases regularly to near 0.