Ising Models on Power-Law Random Graphs |
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Authors: | Sander?Dommers Cristian?Giardinà Remco?van?der?Hofstad |
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Affiliation: | 1.Department of Mathematics and Computer Science,Eindhoven University of Technology,Eindhoven,The Netherlands;2.Modena and Reggio Emilia University,Reggio Emilia,Italy |
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Abstract: | 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. |
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