THE THERMODYNAMICS OF THE CURIE-WEISS MODEL WITH RANDOM COUPLINGS
THE THERMODYNAMICS OF THE CURIE-WEISS MODEL WITH RANDOM COUPLINGS
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DOI：
10.1007/bf01048027
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发表时间：
1993-08-01
影响因子：
1.6
通讯作者：
GAYRARD, V
中科院分区：
文献类型：
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作者：
BOVIER, A;GAYRARD, V
我们研究居里-外斯版本的伊辛自旋系统的随机，正偏置耦合。特别地，考虑了耦合的概率p取1，概率1 - p取0的情况，这描述了随机图上的伊辛模型。我们证明了，如果允许p随着系统大小N以这样的方式减少，即Np（N）向上无穷大作为N向上无穷大，那么自由能收敛（平凡重新标度后）的标准居里-外斯模型，几乎肯定。同样，平均磁化强度的感应措施收敛到居里-外斯模型。这一结果推广到广泛的一类分布的详细说明。
We study the Curie-Weiss version of an Ising spin system with random, positively biased couplings. In particular, the case where the couplings epsilon(ij) take the values one with probability p and zero with probability 1 - p, which describes the Ising model on a random graph, is considered. We prove that if p is allowed to decrease with the system size N in such a way that Np(N) up infinity as N up infinity, then the free energy converges (after trivial rescaling) to that of the standard Curie-Weiss model, almost surely. Similarly, the induced measures on the mean magnetizations converge to those of the Curie-Weiss model. Generalizations of this result to a wide class of distributions are detailed.