Related papers: A simplified Parisi Ansatz II: REM universality
In this paper we present the exact solution for the average minimum energy of the random bipartite matching model with an arbitrary finite number of elements where random paired interactions are described by independent exponential…
We propose a general quantitative scheme in which systems are given the freedom to sacrifice energy equi-partitioning on the relevant time-scales of observation, and have phase transitions by separating autonomously into ergodic sub-systems…
A quantum Parisi formula for the transverse field Sherrington-Kirkpatrick (SK) model is proven with an elementary mathematical method. First, a self-overlap corrected quantum model of the transverse field SK model is represented in terms of…
Random Overlap Structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits…
In an earlier work, the statistical physics associated with finite--temperature decoding of code ensembles, along with the relation to their random coding error exponents, were explored in a framework that is analogous to Derrida's random…
Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond $N \sim 100$ spins has remained computationally challenging. We use quantum annealing to access ground states of…
Spin glass models involving multiple replicas with constrained overlaps have been studied in [FPV92; PT07; Pan18a]. For the spherical versions of these models [Ko19; Ko20] showed that the limiting free energy is given by a Parisi type…
We consider a sequence of random Hamiltonians $H_n(h,\sigma)=\sum^n_{i=1}h_i(\sigma_i-m)$, and study the asymptotic ($n\to \infty$) distribution of the energy levels $(H_n(h,\sigma))_{\sigma\in \{-1,1\}^n}$, where $h_1,h_2,\cdots$ are…
We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the…
We introduce the concept of Random Multi-Overlap Structures in diluted spin glasses, following the ideas of Aizenman, Sims and Starr for non-diluted models. As a result, we prove the generalized bound and variational principle for the free…
Three-dimensional icosahedral random tilings with rhombohedral cells are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasilattice points in the orthogonal space. The internal…
We compute the pressure of the random energy model (REM) and generalized random energy model(GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra's ``broken replica symmetry bounds",and…
We propose a general scheme in which disordered systems are allowed to sacrifice energy equi-partitioning and separate into a hierarchy of ergodic sub-systems (clusters) with different characteristic time-scales and temperatures. The…
We introduce here a new universality conjecture for levels of random Hamiltonians, in the same spirit as the local REM conjecture made by S. Mertens and H. Bauke. We establish our conjecture for a wide class of Gaussian and non-Gaussian…
In this chapter we report on the measurements of the overlap distribution of the replica symmetry breaking solution in complex disordered systems. After a general introduction to the problem of the experimental validation of the Parisi…
We introduce a perceptron version of the Generalized Random Energy Model, and prove a quenched Sanov type large deviation principle for the empirical distribution of the random energies. The dual of the rate function has a representation…
Genome-wide association studies have proven to be essential for understanding the genetic basis of disease. However, many complex traits---personality traits, facial features, disease subtyping---are inherently high-dimensional, impeding…
We establish three equivalent versions of a Parisi formula for the free energy of mean-field spin glasses in a transversal magnetic field. These results are derived from available results for classical vector spin glasses by an…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…