Following states in temperature in the spherical<i>s</i>+<i>p</i>-spin glass model

Sun, Yifan; Crisanti, A.; Krząkała, Florent; Leuzzi, Luca; Zdeborová, Lenka

doi:10.1088/1742-5468/2012/07/p07002

Cited by 19 publications

(33 citation statements)

References 27 publications

(118 reference statements)

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“…The findings of [294], however, raised even more questions. It is found by the Nishimori mapping to the model with a ferromagnetic bias (as described in section II B) that there is no FRSB solution to the problem, yet there is no magnetized 1RSB solution at very low temperature either.…”

Section: Following States and Analyzing Slow Annealingmentioning

confidence: 99%

Statistical physics of inference: thresholds and algorithms

Zdeborová

Krząkała

2016

Advances in Physics

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339

443

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Many questions of fundamental interest in today's science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problems, the central scientific questions are: Under what conditions is the information contained in the measurements sufficient for a satisfactory inference to be possible? What are the most efficient algorithms for this task? A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics. Moreover, it turned out that we can use the gained physical insight to develop new promising algorithms. The connection between inference and statistical physics is currently witnessing an impressive renaissance and we review here the current state-of-the-art, with a pedagogical focus on the Ising model which, formulated as an inference problem, we call the planted spin glass. In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear measurements, with compressed sensing as a case of sparse estimation. Our goal is to provide a pedagogical review for researchers in physics and other fields interested in this fascinating topic. arXiv:1511.02476v5 [cond-mat.stat-mech] 22 Jan 2018 2 CONTENTS

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Section: Following States and Analyzing Slow Annealingmentioning

confidence: 99%

Statistical physics of inference: thresholds and algorithms

Zdeborová

Krząkała

2016

Advances in Physics

Self Cite

339

443

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“…The properties of the model depend on the number and the value of the p's in the sum [14][15][16][17][18]. We shall not discuss this issue here, since we are only interested into the general expression of the eigenvalues controlling the stability of saddle point controlling the static, thermodynamic, properties of the model in the thermodynamic limit N → ∞.…”

Section: Gaussian Fluctuations In the Spherical Modelmentioning

confidence: 99%

Replica Fourier Transform: Properties and applications

Crisanti

Dominicis²

2015

Nuclear Physics B

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The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically.

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“…The alerted reader will recognize the similarity of eq.ns (11) with the convolution of two functions in the supersymmetric formalism used in the Langevin relaxational dynamics starting from random initial conditions [14]. In that context one defines the supersymmetric correlation function…”

Section: The Replica Algebramentioning

confidence: 99%

Quasi-equilibrium in glassy dynamics: an algebraic view

Franz

Parisi

2013

J. Stat. Mech.

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We study a chain of identical glassy systems in a constrained equilibrium where each bond of the chain is forced to remain at a preassigned distance to the previous one. We apply this description to Mean Field Glassy systems in the limit of long chain where each bond is close to the previous one. We show that in specific conditions this pseudo-dynamic process can formally describe real relaxational dynamics for long times. In particular, in mean field spin glass models we can recover in this way the equations of Langevin dynamics in the long time limit at the dynamical transition temperature and below. We interpret the formal identity as an evidence that in these situations the configuration space is explored in a quasi-equilibrium fashion. Our general formalism, that relates dynamics to equilibrium, puts slow dynamics in a new perspective and opens the way to the computation of new dynamical quantities in glassy systems.

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Following states in temperature in the sphericals+p-spin glass model

Cited by 19 publications

References 27 publications

Statistical physics of inference: thresholds and algorithms

Statistical physics of inference: thresholds and algorithms

Replica Fourier Transform: Properties and applications

Quasi-equilibrium in glassy dynamics: an algebraic view

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