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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)