The phase diagram of Lévy spin glasses

Abstract

We study the L\\'evy spin-glass model with the replica and the cavity method.\nIn this model each spin interacts through a finite number of strong bonds and\nan infinite number of weak bonds. This hybrid behaviour of L\\'evy spin glasses\nbecomes transparent in our solution: the local field contains a part\npropagating along a backbone of strong bonds and a Gaussian noise term due to\nweak bonds. Our method allows to determine the complete replica symmetric phase\ndiagram, the replica symmetry breaking line and the entropy. The results are\ncompared with simulations and previous calculations using a Gaussian ansatz for\nthe distribution of fields.\n