一类整数自旋系统的相变缺失
Absence of phase transitions in a class of integer spin systems
摘要：
我们给出了一类整数自旋系统，其自由能在任何温度下都可以用绝对收敛的级数表示。这一类包括$\Z^d$上的自旋系统，它们通过无限程对势相互作用，在大距离$r$上以$1/r^{d+\e}$与$\e>0$的速率多项式衰减。它还包含在无序相在大值的晶体场的布卢姆-金刚砂-格里菲斯模型。
英文摘要：
We exhibit a class of integer spin systems whose free energy can be written in term of an absolutely convergent series at any temperature. This class includes spin systems on $\Z^d$ interacting through infinite range pair potential polynomially decaying at large distances $r$ at a rate $1/r^{d+\e}$ with $\e>0$. It also contains the Blume-Emery-Griffiths model in the disordered phase at large values of the crystal field.
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