Loop effects in the Ising spin glass on the Bethe-like lattices

Equations for the spin glass order in the Ising spin glass model on the Bethe-like lattices with and without small loops are studied. For each lattice, equations are obtained by using and not using the replica method. Within the replica symmetric approximation, equations obtained by the two ways are shown to be identical. To see the effects of the small loops and the replica symmetry breaking, a spin glass order parameter is investigated as a function of the connectivity of the lattices close to the transition temperature. Replica symmetry breaking is enhanced by the existence of small loops.