Jean-Marie Maillard et al 2003 J. Phys. A: Math. Gen. 36 9799 doi:10.1088/0305-4470/36/38/301
Jean-Marie Maillard1, Koji Nemoto2 and Hidetoshi Nishimori3
Show affiliationsWe 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 special simplicities under such conditions. Using these duality and symmetry arguments we present a conjecture on the exact location of the multicritical point in the phase diagram.
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.)
Issue 38 (26 September 2003)
Received 6 June 2003
Published 10 September 2003
Jean-Marie Maillard et al 2003 J. Phys. A: Math. Gen. 36 9799
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