Absence of glassy behaviour in the deterministic spherical and XY models

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

Research output: Contribution to journalArticle

Abstract

We consider the infinite-range spin models with Hamiltonian H = ∑N i, 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
Volume31
Issue number4
DOIs
StatePublished - Jan 30 1998

Fingerprint

Spherical Model
XY Model
Deterministic Model
Free Energy
Gibbs free energy
Spin Models
Ground State
Hamiltonians
Quantization
Torus
Trivial
Ground state
Range of data
ground state

ASJC Scopus subject areas

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

Cite this

Absence of glassy behaviour in the deterministic spherical and XY models. / Borsari, I.; Camia, Federico; Graffi, S.; Unguendoli, F.

In: Journal of Physics A: Mathematical and General, Vol. 31, No. 4, 30.01.1998, p. 1127-1139.

Research output: Contribution to journalArticle

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