Solvable spin systems with random interactions

Abel Klein

Nicola Kistler

We show that spin systems with two body, generic (ferro- or paramagnetic, or random) interactions are 'completely integrable'. The approach is worked out, by way of example, for the Sherrington Kirkpatrick model: we derive an exact, closed formula for the quenched free energy in finite volume which involves an integral over a Gaussian field with correlation structure given by the interaction matrix (with a twist).

Seiichiro Katsura

The random-bond Ising model with continuous (rectangular) distribution of exchange interactions is treated in the Bethe approximation and is shown to have the glass-like phase. The phase diagram similar to that by Sherrington and Kirkpatrick (1975) is obtained. The random-bond Ising model on the infinite Bethe lattice is regarded as an exactly solvable model showing the spin glass.

Yutaka Okabe, Kazuhisa Kaneda, Yusuke Tomita +5 more

Man Mohan

Oleg Derzhko, Johannes Richter

This paper presents exact calculations of thermodynamic quantities for the spin- isotropic XY chain with random Lorentzian intersite interaction and transverse field that depends linearly on the surrounding intersite interactions.