Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices

Details Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices

2007-08-14

arxiv.org/abs/0708.1889v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

20 pages, 10 figures (v3: Corrected analysis of transitions. Appendix proof fixed)

Scientific paper

10.1140/epjb/e2008-00221-y

We solve the Edwards-Anderson model (EA) in different Husimi lattices. We show that, at T=0, the structure of the solution space depends on the parity of the loop sizes. Husimi lattices with odd loop sizes have always a trivial paramagnetic solution stable under 1RSB perturbations while, in Husimi lattices with even loop sizes, this solution is absent. The range of stability under 1RSB perturbations of this and other RS solutions is computed analytically (when possible) or numerically. We compute the free-energy, the complexity and the ground state energy of different Husimi lattices at the level of the 1RSB approximation. We also show, when the fraction of ferromagnetic couplings increases, the existence, first, of a discontinuous transition from a paramagnetic to a spin glass phase and latter of a continuous transition from a spin glass to a ferromagnetic phase.

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