Zero temperature solutions of the Edwards-Anderson model in random Husimi lattices
Henri-Poincaré Group of Complex Systems, Physics Faculty, University of Havana, La Habana, CP 10400, Cuba and Department of Theoretical Physics, Physics Faculty, University of Havana, La Habana, CP 10400, Cuba
Published online: 6 June 2008
We solve the Edwards-Anderson model (EA) in different Husimi lattices using the cavity method at replica symmetric (RS) and 1-step of replica symmetry breaking (1RSB) levels. 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 may have a trivial paramagnetic solution thermodynamically relevant for highly frustrated systems 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 also study the transition from 1RSB solutions to paramagnetic and ferromagnetic RS solutions. Finally we compare the solutions of the EA model in Husimi lattices with that on the (short loops free) Bethe lattices, showing that already for loop sizes of order 8 both models behave similarly.
PACS: 75.10.Nr – Spin-glass and other random models / 75.40.Cx – Static properties / 05.70.Fh – Phase transitions: general studies / 64.60.aq – Networks
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008