Ising spin glass on Bethe-like lattices

Yokota, Terufumi   

Ising spin glass on Bethe-like lattices is studied focusing on the replica symmetry breaking. To see the frustration effects of small loops, spin glass order parameter functions and the AT lines are obtained for the Bethe-like cactus lattices. They are compared with the results for the Bethe lattice without small loops to see the effects of the loops. Triangular, tetrahedral and square cactus lattices are studied. The slope of the spin glass order parameter function for a cactus lattice is smaller than the corresponding one for the Bethe lattice. The replica symmetry breaking region in fields for the cactus lattice is larger than that for the corresponding Bethe lattice except for the smallest number of connectivity of the loops in the triangular and tetrahedral cactus lattices. To obtain the results, an equation among quantities that are related to the spin glass order parameter is used. This equation is shown to be related to an equation derived without using replicas.