Ground states for a class of deterministic spin models with glassy behaviour

Abstract

We consider the deterministic model with glassy behaviour, recently introduced by Marinari, Parisi and Ritort, with \ha\ $H={\sum }_{i,j=1}^N{J}_{i,j}{\sigma }_i{\sigma }_j$, where $J$ is the discrete sine Fourier transform. The ground state found by these authors for $N$ odd and $2N+1$ prime is shown to become asymptotically dege\-ne\-ra\-te when $2N+1$ is a product of odd primes, and to disappear for $N$ even. This last result is based on the explicit construction of a set of eigenvectors for $J$, obtained through its formal identity with the imaginary part of the propagator of the quantized unit symplectic matrix over the $2$-torus.

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References in corpus (4)

• Replica Field Theory for Deterministic Models (II): A Non-Random Spin Glass with Glassy Behavior
• Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation
• Self Induced Quenched Disorder: A Model for the Glass Transition
• Mean-Field Equations for Spin Models with Orthogonal Interaction Matrices

Cited by in corpus (2)

• On the ground states of the Bernasconi model
• Deterministic spin models with a glassy phase transition