A simplified Parisi Ansatz II: REM universality
arXiv:2312.07808 · doi:10.1016/j.chaos.2024.115821
Abstract
In a previous work [A simplified Parisi Ansatz, Franchini, S., Commun. Theor. Phys., 73, 055601 (2021)] we introduced a simple method to compute the Random Overlap Structure of Aizenmann, Simm and Stars and the full RSB Parisi formula for the Sherrington-Kirkpatrick Model without using replica theory. The method consists in partitioning the system into smaller sub-systems that we call layers, and iterate the Bayes rule. A central ansatz in our derivation was that these layers could be approximated by Random Energy Models of the Derrida type. In this paper we analyze the properties of the interface in detail, and show the equivalence with the Random Energy Model at any temperature.
Respect to the published version: we identify and correct a mistake in evaluating the function in Eq. (15). 35 pages, 1 figure
References in corpus (15)
- Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
- Experimental evidence of replica symmetry breaking in random lasers
- Random Costs in Combinatorial Optimization
- Number partitioning as random energy model
- Mean-field model for the density of states of jammed soft spheres
- The Exponential Capacity of Dense Associative Memories
- Mapping of attention mechanisms to a generalized Potts model
- Large deviations for Generalized Polya Urns with arbitrary urn function
- Large deviations in models of growing clusters with symmetry-breaking transitions
- Neural activity in quarks language: Lattice Field Theory for a network of real neurons
- Large Deviations Theory of Increasing Returns
- Replica Symmetry Breaking without Replicas
- Random Polymers and Generalized Urn Processes
- Contributions to Random Energy Models
- Dissecting the Interplay of Attention Paths in a Statistical Mechanics Theory of Transformers