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arXiv · 1702.02338

Cusp singularity in mean field Ising model

Yayoi Abe·Muneyuki Ishida·Erika Nozawa·Takayoshi Ootsuka·Ryoko Yahagi
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Abstract

An entropy of the Ising model in the mean field approximation is derived by the Hamilton-Jacobi formalism. We consider a grand canonical ensemble with respect to the temperature and the external magnetic field. A cusp arises at the critical point, which shows a simple and new geometrical aspect of this model. In educational sense, this curve with a cusp helps students acquire a more intuitive view on statistical phase transitions.

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Yayoi Abe, Muneyuki Ishida, Erika Nozawa, Takayoshi Ootsuka, Ryoko Yahagi. 2017-02-08. Cusp singularity in mean field Ising model. https://doi.org/10.1088/1361-6404/aa82fc

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