Symmetry, complexity and multicritical point of the two-dimensional spin glass

@article{Maillard2003SymmetryCA,
  title={Symmetry, complexity and multicritical point of the two-dimensional spin glass},
  author={J-M Maillard and Koji Nemoto and Hidetoshi Nishimori},
  journal={Journal of Physics A},
  year={2003},
  volume={36},
  pages={9799-9825}
}
We analyse models of spin glasses on the two-dimensional square lattice by exploiting symmetry arguments. The replicated partition functions of the Ising and related spin glasses are shown to have many remarkable symmetry properties as functions of the edge Boltzmann factors. It is shown that the applications of homogeneous and Hadamard inverses to the edge Boltzmann matrix indicate reduced complexities when the elements of the matrix satisfy certain conditions, suggesting that the system has… 

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