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The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics
Series 8
Volume 35, 1977 - Issue 3
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Original Articles

Solution of 'Solvable model of a spin glass'

D. J. Thouless Department of Mathematical Physics, University of Birmingham, Birmingham, England
,
P. W. Anderson Department of Physics, Princeton University, Princeton, New Jersey, 08540, U.S.A.; Laboratories, Murray Hill, New Jersey, 07974, U.S.A.; Princeton University, partially supported by National Science Foundation Grant No. DMR76-00880
&
R. G. Palmer Department of Physics, Princeton University, Princeton, New Jersey, 08540, U.S.A.
Pages 593-601 | Received 12 Oct 1976, Published online: 13 Sep 2006

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G. Parisi. (1980) The magnetic properties of the Sherrington-Kirkpatrick model for spin glasses. Philosophical Magazine B 41:6, pages 677-680.
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Mutian Shen, Pan Zhang & Hai-Jun Zhou. (2018) Compressed Sensing by Shortest-Solution Guided Decimation. IEEE Access 6, pages 5564-5572.
Crossref
Ada Altieri. (2018) Higher-order corrections to the effective potential close to the jamming transition in the perceptron model. Physical Review E 97:1.
Crossref
Eliran Subag. (2017) The geometry of the Gibbs measure of pure spherical spin glasses. Inventiones mathematicae 210:1, pages 135-209.
Crossref
Juan J Alonso & B Allés. (2017) Nature of the spin-glass phase in dense packings of Ising dipoles with random anisotropy axes. Journal of Physics: Condensed Matter 29:35, pages 355802.
Crossref
Eliran Subag. (2017) The complexity of spherical $p$-spin models—A second moment approach. The Annals of Probability 45:5.
Crossref
Jean Barbier & Florent Krzakala. (2017) Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes. IEEE Transactions on Information Theory 63:8, pages 4894-4927.
Crossref
Thibault Lesieur, Florent Krzakala & Lenka Zdeborová. (2017) Constrained low-rank matrix estimation: phase transitions, approximate message passing and applications. Journal of Statistical Mechanics: Theory and Experiment 2017:7, pages 073403.
Crossref
Jacopo Rocchi, David Saad & Chi Ho Yeung. (2017) Self-sustained clusters as drivers of computational hardness in -spin models . Physical Review B 96:2.
Crossref
Silvio Franz, Giorgio Parisi, Maxime Sevelev, Pierfrancesco Urbani & Francesco Zamponi. (2017) Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems. SciPost Physics 2:3.
Crossref
Ahmed El Alaoui, Aaditya Ramdas, Florent Krzakala, Lenka Zdeborova & Michael I. Jordan. (2017) Decoding from pooled data: Phase transitions of message passing. Decoding from pooled data: Phase transitions of message passing.
Andre Manoel, Florent Krzakala, Marc Mezard & Lenka Zdeborova. (2017) Multi-layer generalized linear estimation. Multi-layer generalized linear estimation.
Thibault Lesieur, Leo Miolane, Marc Lelarge, Florent Krzakala & Lenka Zdeborova. (2017) Statistical and computational phase transitions in spiked tensor estimation. Statistical and computational phase transitions in spiked tensor estimation.
Haiping Huang. (2017) Statistical mechanics of unsupervised feature learning in a restricted Boltzmann machine with binary synapses. Journal of Statistical Mechanics: Theory and Experiment 2017:5, pages 053302.
Crossref
Marc Mézard. (2017) Mean-field message-passing equations in the Hopfield model and its generalizations. Physical Review E 95:2.
Crossref
John A Hertz, Yasser Roudi & Peter Sollich. (2017) Path integral methods for the dynamics of stochastic and disordered systems. Journal of Physics A: Mathematical and Theoretical 50:3, pages 033001.
Crossref
G Mossi, T Parolini, S Pilati & A Scardicchio. (2017) On the quantum spin glass transition on the Bethe lattice. Journal of Statistical Mechanics: Theory and Experiment 2017:1, pages 013102.
Crossref
Christian Donner, Klaus Obermayer & Hideaki Shimazaki. (2017) Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations. PLOS Computational Biology 13:1, pages e1005309.
Crossref
Corrado RainoneCorrado Rainone. 2017. Metastable Glassy States Under External Perturbations. Metastable Glassy States Under External Perturbations 85 97 .
Corrado RainoneCorrado Rainone. 2017. Metastable Glassy States Under External Perturbations. Metastable Glassy States Under External Perturbations 19 47 .
Christophe Schülke, Philip Schniter & Lenka Zdeborová. (2016) Phase diagram of matrix compressed sensing. Physical Review E 94:6.
Crossref
Simon L. Dettmer, H. Chau Nguyen & Johannes Berg. (2016) Network inference in the nonequilibrium steady state. Physical Review E 94:5.
Crossref
L Bachschmid-Romano, C Battistin, M Opper & Y Roudi. (2016) Variational perturbation and extended Plefka approaches to dynamics on random networks: the case of the kinetic Ising model. Journal of Physics A: Mathematical and Theoretical 49:43, pages 434003.
Crossref
Ada Altieri, Silvio Franz & Giorgio Parisi. (2016) The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential. Journal of Statistical Mechanics: Theory and Experiment 2016:9, pages 093301.
Crossref
Jean Barbier, Mohamad Dia, Nicolas Macris & Florent Krzakala. (2016) The mutual information in random linear estimation. The mutual information in random linear estimation.
Thibault Lesieur, Caterina de Bacco, Jess Banks, Florent Krzakala, Cris Moore & Lenka Zdeborova. (2016) Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering. Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering.
David Dahmen, Hannah Bos & Moritz Helias. (2016) Correlated Fluctuations in Strongly Coupled Binary Networks Beyond Equilibrium. Physical Review X 6:3.
Crossref
Eric W Tramel, Angélique Drémeau & Florent Krzakala. (2016) Approximate message passing with restricted Boltzmann machine priors. Journal of Statistical Mechanics: Theory and Experiment 2016:7, pages 073401.
Crossref
Yoshiyuki Kabashima, Florent Krzakala, Marc Mezard, Ayaka Sakata & Lenka Zdeborova. (2016) Phase Transitions and Sample Complexity in Bayes-Optimal Matrix Factorization. IEEE Transactions on Information Theory 62:7, pages 4228-4265.
Crossref
B Bravi, P Sollich & M Opper. (2016) Extended Plefka expansion for stochastic dynamics. Journal of Physics A: Mathematical and Theoretical 49:19, pages 194003.
Crossref
György Szabó & István Borsos. (2016) Evolutionary potential games on lattices. Physics Reports 624, pages 1-60.
Crossref
Manfred Opper, Burak Çakmak & Ole Winther. (2016) A theory of solving TAP equations for Ising models with general invariant random matrices. Journal of Physics A: Mathematical and Theoretical 49:11, pages 114002.
Crossref
Andrea Montanari & Emile Richard. (2016) Non-Negative Principal Component Analysis: Message Passing Algorithms and Sharp Asymptotics. IEEE Transactions on Information Theory 62:3, pages 1458-1484.
Crossref
Jin Tan, Yanting Ma, Hoover Rueda, Dror Baron & Gonzalo R. Arce. (2016) Compressive Hyperspectral Imaging via Approximate Message Passing. IEEE Journal of Selected Topics in Signal Processing 10:2, pages 389-401.
Crossref
T. Aspelmeier, Helmut G. Katzgraber, Derek Larson, M. A. Moore, Matthew Wittmann & Joonhyun Yeo. (2016) Finite-size critical scaling in Ising spin glasses in the mean-field regime. Physical Review E 93:3.
Crossref
Jianqiang Li & Fei Wang. (2016) Semi-supervised learning via mean field methods. Neurocomputing 177, pages 385-393.
Crossref
B. Kryzhanovsky & M. Malsagov. (2016) The spectra of local minima in spin-glass models. Optical Memory and Neural Networks 25:1, pages 1-15.
Crossref
K. Y. Michael WONG, David SAAD & Chi Ho YEUNG. (2016) Distributed Optimization in Transportation and Logistics Networks. IEICE Transactions on Communications E99.B:11, pages 2237-2246.
Crossref
Jie Lin & Matthieu Wyart. (2016) Mean-Field Description of Plastic Flow in Amorphous Solids. Physical Review X 6:1.
Crossref
Chengjiang Long, Gang Hua & Ashish Kapoor. (2015) A Joint Gaussian Process Model for Active Visual Recognition with Expertise Estimation in Crowdsourcing. International Journal of Computer Vision 116:2, pages 136-160.
Crossref
Christian Donner & Hideaki Shimazaki. 2016. Neural Information Processing. Neural Information Processing 104 110 .
Marco Baity JesiMarco Baity Jesi. 2016. Spin Glasses. Spin Glasses 115 138 .
Marco Baity JesiMarco Baity Jesi. 2016. Spin Glasses. Spin Glasses 3 42 .
Ryan R. Cheng, Mohit Raghunathan, Jeffrey K. Noel & José N. Onuchic. (2015) Constructing sequence‐dependent protein models using coevolutionary information. Protein Science 25:1, pages 111-122.
Crossref
Jin Tan, Yanting Ma, Hoover Rueda, Dror Baron & Gonzalo R. Arce. (2015) Approximate message passing in coded aperture snapshot spectral imaging. Approximate message passing in coded aperture snapshot spectral imaging.
Silvio FranzGiorgio ParisiPierfrancesco UrbaniFrancesco Zamponi. (2015) Universal spectrum of normal modes in low-temperature glasses. Proceedings of the National Academy of Sciences 112:47, pages 14539-14544.
Crossref
Christophe Schülke, Francesco Caltagirone & Lenka Zdeborová. (2015) Blind sensor calibration using approximate message passing. Journal of Statistical Mechanics: Theory and Experiment 2015:11, pages P11013.
Crossref
J. M. Luck & A. Mehta. (2015) Universality in survivor distributions: Characterizing the winners of competitive dynamics. Physical Review E 92:5.
Crossref
Samiyeh Mahmoudian, Shao Tang & Vladimir Dobrosavljević. (2015) Quantum criticality at the Anderson transition: A typical medium theory perspective. Physical Review B 92:14.
Crossref
Thibault Lesieur, Florent Krzakala & Lenka Zdeborova. (2015) MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel. MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel.

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