Absence of glassy behaviour in the deterministic spherical and XY models

I. Borsari, F. Camia, S. Graffi, F. Unguendoli

Research output: Contribution to journalArticlepeer-review


We consider the infinite-range spin models with Hamiltonian H = ∑Ni, j = 1 Ji, jσiσj, where J is the quantization of a map of the torus. Although deterministic, these models are known to exhibit glassy behaviour. We show, through explicit computation of the Gibbs free energy, that unlike the random case this behaviour disappears in the corresponding spherical and continuous XY models. The only minimum of the Gibbs free energy is indeed the trivial one, even though the ground state is highly degenerate.

Original languageEnglish (US)
Pages (from-to)1127-1139
Number of pages13
JournalJournal of Physics A: Mathematical and General
Issue number4
StatePublished - Jan 30 1998

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy


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