Structure of 1-RSB asymptotic Gibbs measures in the diluted p-spin models

Abstract

In this paper we study asymptotic Gibbs measures in the diluted p-spin models in the so called 1-RSB case, when the overlap takes two values $q_{\ast },q^{\ast }\in [0,1].$ When the external field is not present and the overlap is not equal to zero, we prove that such asymptotic Gibbs measures are described by the Mézard-Parisi ansatz conjectured in [MP]. When the external field is present, we prove that the overlap can not be equal to zero and all 1-RSB asymptotic Gibbs measures are described by the Mézard-Parisi ansatz. Finally, we give a characterization of the exceptional case when there is no external field and the smallest overlap value is equal to zero, although it does not go as far as the Mézard-Parisi ansatz. Our approach is based on the cavity computations combined with the hierarchical exchangeability of pure states.

References in corpus (1)

• A hierarchical version of the de Finetti and Aldous-Hoover representations

Cited by in corpus (7)

• Charting the replica symmetric phase
• Structure of finite-RSB asymptotic Gibbs measures in the diluted spin glass models
• On the overlap distribution of branching random walks
• Free energy of a diluted spin glass model with quadratic Hamiltonian
• Mean Field Spin Glass Models under Weak External Field
• Replica bound for Ising spin glass models in one dimension
• On the replica symmetry phase of the independent set problem