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..

Ground states for a class of deterministic spin models with glassy behaviour / I., Borsari; S., Graffi; Unguendoli, Francesco. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - STAMPA. - 29:(1996), pp. 1593-1604.

### 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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1604
Ground states for a class of deterministic spin models with glassy behaviour / I., Borsari; S., Graffi; Unguendoli, Francesco. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - STAMPA. - 29:(1996), pp. 1593-1604.
I., Borsari; S., Graffi; Unguendoli, Francesco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/611767
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