Scheme of the replica symmetry breaking for short- ranged Ising spin glass within the Bethe- Peierls method

Abstract

Within the Bethe- Peierls method the for short- ranged Ising spin glass, recently formulated by Serva and Paladin, the equation for the spin glass parameter function near the transition to the paramagnetic phase has been carried out. The form of this equation is qualitatively similar to that for Sherrington- Kirpatrick model, but quantitatively the order parametr function depends of the dimension d of the system. In the case d tends to infinity one obtains well known Parisi solution.