Cusp singularity in mean field Ising model

@article{Abe2017CuspSI,
  title={Cusp singularity in mean field Ising model},
  author={Yayoi Abe and M. Ishida and Erika Nozawa and T. Ootsuka and R. Yahagi},
  journal={arXiv: Mathematical Physics},
  year={2017}
}
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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