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Related papers: A replica trick for rare samples

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We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The…

Disordered Systems and Neural Networks · Physics 2009-10-31 L. B. Ioffe , A. V. Lopatin

In this paper we adapt the broken replica interpolation technique (developed by Francesco Guerra to deal with the Sherrington-Kirkpatrick model, namely a pairwise mean-field spin-glass whose couplings are i.i.d. standard Gaussian variables)…

Mathematical Physics · Physics 2020-06-02 Elena Agliari , Linda Albanese , Adriano Barra , Gabriele Ottaviani

In this paper, we consider an importance sampling problem for a certain rare-event simulations involving the behavior of a diffusion process pertaining to a chain of distributed systems with random perturbations. We also assume that the…

Optimization and Control · Mathematics 2020-08-26 Getachew K. Befekadu

We study the problem of testing and recovering $k$-clique Ferromagnetic mean shift in the planted Sherrington-Kirkpatrick model (i.e., a type of spin glass model) with $n$ spins. The planted SK model -- a stylized mixture of an uncountable…

Statistics Theory · Mathematics 2024-03-25 Yihan He , Han Liu , Jianqing Fan

For a very general class of probability distributions in disordered Ising spin systems, in the thermodynamical limit, we prove the following property for overlaps among real replicas. Consider the overlaps among s replicas. Add one replica…

Disordered Systems and Neural Networks · Physics 2009-10-31 Stefano Ghirlanda , Francesco Guerra

A framework for the investigation of disordered quantum systems in thermal equilibrium is proposed. The approach is based on a dynamical model--which consists of a combination of a double-bracket gradient flow and a uniform Brownian…

Quantum Physics · Physics 2013-09-13 Dorje C. Brody , David C. P. Ellis , Darryl D. Holm

We extend to quenched disordered systems the variational scheme for real space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow…

Statistical Mechanics · Physics 2020-11-11 Yantao Wu , Roberto Car

We review the approach to glasses based on the replica formalism. The replica approach presented here is a first principle's approach which aims at deriving the main glass properties from the microscopic Hamiltonian. In contrast to the old…

Disordered Systems and Neural Networks · Physics 2009-10-16 Marc Mezard , Giorgio Parisi

We discuss replica analytic continuation using several simple models in order to prove mathematically the validity of replica analysis, which is used in a wide range of fields related to large scale complex systems. While replica analysis…

Disordered Systems and Neural Networks · Physics 2016-06-24 Takashi Shinzato

Using results of a Monte Carlo simulation of the Sherrington-Kirkpatrick model, we try to characterize the slow disorder samples, namely we analyze visually the correlation between the relaxation time for a given disorder sample $J$ with…

Disordered Systems and Neural Networks · Physics 2015-03-17 Alain Billoire

We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation…

Disordered Systems and Neural Networks · Physics 2016-10-19 Hugo Jacquin , A. Rancon

We propose a coupled rejection-sampling method for sampling from couplings of arbitrary distributions. The method relies on accepting or rejecting coupled samples coming from dominating marginals. Contrary to existing acceptance-rejection…

Methodology · Statistics 2022-03-11 Adrien Corenflos , Simo Särkkä

We consider a system composed by N atoms trapped within a multimode cavity, whose theoretical description is captured by a disordered multimode Dicke model. We show that in the resonant, zero field limit the system exactly realizes the…

Disordered Systems and Neural Networks · Physics 2015-01-16 Pietro Rotondo , Enrico Tesio , Sergio Caracciolo

We study the statistics of thermodynamic quantities in two related systems with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in a random potential and the 2-dimensional random bond dimer model. The first system is…

Disordered Systems and Neural Networks · Physics 2009-11-10 Simon Bogner , Thorsten Emig , Ahmed Taha , Chen Zeng

We propose a new method for estimating rare event probabilities when independent samples are available. It is assumed that the underlying probability measures satisfy a large deviations principle with a scaling parameter $\varepsilon$ that…

Probability · Mathematics 2018-11-06 Paul Dupuis , Guo-Jhen Wu , Michael Snarski

We consider Ising mixed $p$-spin glasses at high-temperature and without external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We develop a new sampling algorithm with complexity of the same…

Probability · Mathematics 2025-10-22 Ahmed El Alaoui , Andrea Montanari , Mark Sellke

Population annealing is a variant of the simulated annealing algorithm that improves the quality of the thermalization process in systems with rough free-energy landscapes by introducing a resampling process. We consider the diluted…

Statistical Mechanics · Physics 2025-08-26 Fernando Martínez-García , Diego Porras

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…

Disordered Systems and Neural Networks · Physics 2016-08-24 David Dahmen , Hannah Bos , Moritz Helias

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica…

Disordered Systems and Neural Networks · Physics 2009-04-30 D. B. Liarte , S. R. Salinas , C. S. O. Yokoi

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely…

Disordered Systems and Neural Networks · Physics 2013-05-29 Jack Raymond , David Saad