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We consider the mixed $p$-spin mean-field spin glass model with Ising spins and investigate its free energy in the spirit of the TAP approach, named after Thouless, Anderson, and Palmer.
The overlap gap property and approximate message passing algorithms for p-spin models
D. Gamarnik and A. Jagannath · 1911
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Solvable model of a spin glass
D. Sherrington and S. Kirkpatrick · 1975
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Solution of ‘solvable model of a spin glass’
D. J. Thouless, P. W. Anderson, and R. G. Palmer · 1977
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Infinite number of order parameters for spin-glasses
G. Parisi · 1979
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A sequence of approximate solutions to the S-K model for spin glasses
G. Parisi · 1980
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Convergence condition of the TAP equation fo the infinite-ranged Ising spin glass model
T. Plefka · 1982
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On the nature of the spin-glass phase
M. Mézard, G. Parisi, N. Sourlas, G. Toulouse, and M.A. Virasoro · 1984
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Replica symmetry breaking and the nature of the spin-glass phase
M. Mézard, G. Parisi, N. Sourlas, G. Toulouse, and M.A. Virasoro · 1984
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The microstructure of ultrametricity
M. Mézard and M.A. Virasoro · 1985
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Spin glass theory and beyond
M. Mézard, G. Parisi, and M. A. Virasoro · 1987
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A mathematical reformulation of Derrida’s REM and GREM
D. Ruelle · 1987
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The number of solutions of the Thouless-Anderson-Palmer equations for p p -spin-interaction spin glasses
H. Rieger · 1992
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Thouless-Anderson-Palmer approach to the spherical p p -spin spin glass model
A. Crisanti and H.-J. Sommers · 1995
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The thermodynamic limit in mean field spin glass models
F. Guerra and F. Toninelli · 2002
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The complexity of the spherical p p -spin spin glass model, revisited
A. Crisanti, L. Leuzzi, and T. Rizzo · 2003
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Broken replica symmetry bounds in the mean field spin glass model
F. Guerra · 2003
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Low-degree hardness of random optimization problems
D. Gamarnik, A. Jagannath, and A. S. Wein · 2004
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Complexity in mean-field spin-glass models: Ising p p -spin
A. Crisanti, L. Leuzzi, and T. Rizzo · 2005
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Free energy in the generalized Sherrington–Kirkpatrick mean field model
D. Panchenko · 2005
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The Parisi formula
M. Talagrand · 2006
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Parisi measures
M. Talagrand · 2006
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Mean-field spin glass models from the cavity-ROSt perspective
M. Aizenman, R. Sims, and S. L. Starr · 2007
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Spin glasses and Stein’s method
S. Chatterjee · 2010
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Construction of pure states in mean field models for spin glasses
M. Talagrand · 2010
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Mean field models for spin glasses. Volume I
M. Talagrand · 2011
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Mean field models for spin glasses. Volume II
M. Talagrand · 2011
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Random matrices and complexity of spin glasses
A. Auffinger, G. Ben Arous, and J. Černý · 2013
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The Aizenman-Sims-Starr scheme and Parisi formula for mixed p p -spin spherical models
W.-K. Chen · 2013
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The Parisi ultrametricity conjecture
Variational representations for the Parisi functional and the two-dimensional Guerra-Talagrand bound
W.-K. Chen · 2017
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Approximate ultrametricity for random measures and applications to spin glasses
A. Jagannath · 2017
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On the unbalanced cut problem and the generalized Sherrington-Kirkpatrick model
A. Jagannath and S. Sen · 2017
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Some properties of the phase diagram for mixed p p -spin glasses
A. Jagannath and I. Tobasco · 2017
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Estimation of law-rank matrices via approximate message passing
A. Montanari and R. Venkataramanan · 2017
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The complexity of spherical p p -spin models—A second moment approach
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D. Panchenko · 2013
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The Sherrington-Kirkpatrick model
D. Panchenko · 2013
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An iterative construction of solutions of the TAP equations for the Sherrington-Kirkpatrick model
E. Bolthausen · 2014
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Superconcentration and related topics
S. Chatterjee · 2014
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Chaos in the mixed even-spin models
W.-K. Chen · 2014
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The Parisi formula for mixed p p -spin models
D. Panchenko · 2014
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E. Subag · 2017
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The geometry of the Gibbs measure of pure spherical spin glasses
E. Subag · 2017
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The extremal process of critical points of the pure p p -spin spherical spin glass model
E. Subag and O. Zeitouni · 2017
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On concentration properties of disordered Hamiltonians
A. Auffinger and W.-K. Chen · 2018
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On spin distributions for generic p p -spin models
A. Auffinger and A. Jagannath · 2018
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On the energy landscape of the mixed even p-spin model
W.-K. Chen, M. Handschy, and G. Lerman · 2018
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On the TAP free energy in the mixed p p -spin models
W.-K. Chen and D. Panchenko · 2018
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Optimization of the Sherrington-Kirkpatrick hamiltonian
A. Montanari · 2018
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Bonus chapter to “The Sherrington-Kirkpatrick model”
D. Panchenko · 2018
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Free energy in the mixed p p -spin models with vector spins
D. Panchenko · 2018
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Free energy in the Potts spin glass
D. Panchenko · 2018
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Free energy landscapes in spherical spin glasses
E. Subag · 2018
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Thouless-Anderson-Palmer equations for generic p p -spin glasses
A. Auffinger and A. Jagannath · 2019
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The TAP-Plefka variational principle for the spherical SK model
D. Belius and N. Kistler · 2019
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Suboptimality of local algorithms for a class of max-cut problems
W.-K. Chen, D. Gamarnik, D. Panchenko, and M. Rahman · 2019
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The generalized TAP free energy II
W.-K. Chen, D. Panchenko, and E. Subag · 2019
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Optimization of mean-field spin glasses
A. El Alaoui, A. Montanari, and M. Sellke · 2020
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