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

Jean Marie Maillard, Koji Nemoto, Hidetoshi Nishimori

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


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 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.

Original languageEnglish
Pages (from-to)9799-9825
Number of pages27
JournalJournal of Physics A: Mathematical and General
Issue number38
Publication statusPublished - 2003 Sep 26
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)


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