Ising Models on Power-Law Random Graphs
Ising Models on Power-Law Random Graphs
复制标题
幂律随机图上的 Ising 模型
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
R. Hofstad
中科院分区：
文献类型：
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作者：
S. Dommers;C. Giardinà;R. Hofstad
研究了度分布为幂律分布的随机图上的铁磁Ising模型，计算了平均度为有限（度指数τ>2）且随机图具有树状结构时的压力热力学极限.为此，我们密切关注Dembo和Montanari的分析（Ann. Appl. Probab. 20（2）：565-592，2010），其假设有限方差度（τ>3），在必要时对其进行调整，并且在可能时对其进行简化。我们的结果也适用于度分布不服从幂律的情况，并进一步确定了各种物理量，如磁化强度和内能的热力学极限。
We study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite (degree exponent τ>2), for which the random graph has a tree-like structure. For this, we closely follow the analysis by Dembo and Montanari (Ann. Appl. Probab. 20(2):565–592, 2010) which assumes finite variance degrees (τ>3), adapting it when necessary and also simplifying it when possible. Our results also apply in cases where the degree distribution does not obey a power law.We further identify the thermodynamic limits of various physical quantities, such as the magnetization and the internal energy.