### Abstract

We consider the infinite-range spin models with Hamiltonian H = ∑^{N} _{i, j = 1} J_{i, j}σ_{i}σ_{j}, 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 language | English (US) |
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Pages (from-to) | 1127-1139 |

Number of pages | 13 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 31 |

Issue number | 4 |

DOIs | |

State | Published - Jan 30 1998 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*31*(4), 1127-1139. https://doi.org/10.1088/0305-4470/31/4/004

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 31, no. 4, pp. 1127-1139. https://doi.org/10.1088/0305-4470/31/4/004

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TY - JOUR

T1 - Absence of glassy behaviour in the deterministic spherical and XY models

AU - Borsari, I.

AU - Camia, Federico

AU - Graffi, S.

AU - Unguendoli, F.

PY - 1998/1/30

Y1 - 1998/1/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0038929406&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038929406&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/31/4/004

DO - 10.1088/0305-4470/31/4/004

M3 - Article

AN - SCOPUS:0038929406

VL - 31

SP - 1127

EP - 1139

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 4

ER -