The full replica symmetry breaking solution in mean-field spin glass models
arXiv:1911.00557
Abstract
This thesis focus on the extension of the Parisi full replica symmetry breaking solution to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-Mézard cavity method, providing a well-defined formulation of the full replica symmetry breaking problem in random regular graphs. We obtain a variational free energy functional, defined by the sum of two variational functionals (auxiliary variational functionals), that are an extension of the Parisi functional of the Sherrington-Kirkpatrick model. We study the properties of the two variational functionals in detailed, providing representation through the solution of a proper backward stochastic differential equation, that generalize the Parisi partial differential equation. Finally, we define the order parameters of the system and get a set of self-consistency equations for the order parameters and free energy.
arXiv commentThesis, 2019
References in corpus (13)
- The Bethe lattice spin glass revisited
- Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
- Functional Itô calculus and stochastic integral representation of martingales
- An Extended Variational Principle for the SK Spin-Glass Model
- Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
- The Parisi formula has a unique minimizer
- Replica bounds for diluted non-Poissonian spin systems
- Spin glass models from the point of view of spin distributions
- Elusive Glassy Phase in the Random Field Ising Model
- Spin Glass Computations and Ruelle's Probability Cascades
- Structure of finite-RSB asymptotic Gibbs measures in the diluted spin glass models
- The marginally stable Bethe lattice spin glass revisited
- The full replica symmetry breaking in the Ising spin glass on random regular graph