On a theory of spin glasses with finite range of interactions

Alain H. Billoire

Luca Leuzzi, Giorgio Parisi A, Federico Ricci‐Tersenghi +1 more

We introduce a diluted version of the one-dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model, varying the power corresponds to changing the dimension in short-range models. The spin-glass phase is studied in and out of the range of validity of the mean-field approximation in order to discriminate between different theories. Since each variable interacts only with a finite number of others the cost for simulating, the model is drastically reduced with respect to the fully connected version, and larger sizes can be studied. We find both static and dynamic indications in favor of the so-called replica symmetry breaking theory.

Andrew Canning, Bruce M. Forrest

A mean-field replica-type theory is presented for long-range Ising spin-glasses whose interactions can be written in the form J ij = J ij I J ij SK , where J SK is a quenched Gaussian interaction, as in the SK spin-glass, and J I is a deterministic matrix which defines the structure or inhomogeneity of the model and must have a finite rank in the thermodynamic limit. The spin-glass model proposed by Franz, Parisi and Virasoro ( Europhys. Lett. , 17 (1992) 5) can be written in this form, with J I having rank 2, and is used as a case study to illustrate our theory. In the context of replica theory we also consider the stable states of this model, which appear continuously as the temperature is lowered.

秀稔 西森, Hidetoshi Nishimori, 毅彦 溝口 +2 more

Imre Kondor

M. V. Feigel’man, L. B. Ioffe

The analytical theory of slow relaxation of the Ising and vector 3-D spin glasses with the finite range interaction near the freezing transition point Tf has been developed. In the Ising case, the maximum relaxation time tmax increases as tmax ∼ ( T - Tf)-6 exp[C(T - T f)-1/4]. For the Heisenberg spins tmax ∼ (T - T f)-10.5. It is shown that the inclusion of weak random-anisotropy exchange leads to the Ising asymptotics for t max in the Heisenberg spin glass.