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.
We further identify the thermodynamic limits of various physical quantities, such as the magnetization and the internal energy.
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Dommers, S., Giardinà, C. & van der Hofstad, R. Ising Models on Power-Law Random Graphs. J Stat Phys 141, 638–660 (2010). https://doi.org/10.1007/s10955-010-0067-9
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DOI: https://doi.org/10.1007/s10955-010-0067-9