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We introduce and analyze free energy landscapes defined by associating to any point inside the sphere a free energy calculated on a thin spherical band around it, using many orthogonal replicas.
The Brunn-Minkowski inequality in Gauss space
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Solvable model of a spin glass
D. Sherrington and S. Kirkpatrick · 1975
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Norms of Gaussian sample functions
B. S. Cirel ′ · 1976
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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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Metastable states in spin glasses
A. J. Bray and M. A. Moore · 1980
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A sequence of approximated solutions to the s-k model for spin glasses
G. Parisi · 1980
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Convergence condition of the TAP equation for the infinite-ranged Ising spin glass model
T. Plefka · 1982
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Weighted averages and order parameters for the infinite range Ising spin glass
C. De Dominicis and A. P. Young · 1983
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Order parameter for spin-glasses
G. Parisi · 1983
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The simplest spin glass
D. J. Gross and M. Mezard · 1984
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Nature of the spin-glass phase
M. Mézard, G. Parisi, N. Sourlas, G. Toulouse, and M. 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. Virasoro · 1984
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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 spherical p-spin interaction spin glass model: the statics
A. Crisanti and H.-J. Sommers · 1992
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The number of solutions of the thouless-anderson-palmer equations for p
H. Rieger · 1992
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Barriers and metastable states as saddle points in the replica approach
J. Kurchan, G. Parisi, and M. A. Virasoro · 1993
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Thouless-anderson-palmer approach to the spherical p-spin spin glass model
A. Crisanti and H.-J. Sommers · 1995
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On the stability of the quenched state in mean-field spin-glass models
M. Aizenman and P. Contucci · 1998
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On Ruelle’s probability cascades and an abstract cavity method
E. Bolthausen and A.-S. Sznitman · 1998
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Stationary points of the thouless-anderson-palmer free energy
A. Cavagna, I. Giardina, and G. Parisi · 1998
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General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity
S. Ghirlanda and F. Guerra · 1998
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Some exact results on the ultrametric overlap distribution in mean field spin glass models (i)
F. Baffioni and F. Rosati · 2000
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Extended variational principle for the Sherrington-Kirkpatrick spin-glass model
M. Aizenman, R. Sims, and S. L. Starr · 2003
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On the formal equivalence of the TAP and thermodynamic methods in the SK model
A. Cavagna, I. Giardina, G. Parisi, and M. Mézard · 2003
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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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Complexity of ising spin glasses
T. Aspelmeier, A. J. Bray, and M. A. Moore · 2004
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Derrida’s generalised random energy models. I. Models with finitely many hierarchies
A. Bovier and I. Kurkova · 2004
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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
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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Temperature chaos in some spherical mixed p p -spin models
W.-K. Chen and D. Panchenko · 2017
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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 of the spherical mean field model
M. Talagrand · 2006
Cited alongside, same era.
The Parisi formula
M. Talagrand · 2006
Cited alongside, same era.
Random fields and geometry
R. J. Adler and J. E. Taylor · 2007
Cited alongside, same era.
Mean-field spin glass models from the cavity-ROSt perspective
M. Aizenman, R. Sims, and S. L. Starr · 2007
Cited alongside, same era.
On the overlap in the multiple spherical SK models
D. Panchenko and M. Talagrand · 2007
Cited alongside, same era.
Parisi formula, disorder chaos and fluctuation for the ground state energy in the spherical mixed p p -spin models
W.-K. Chen and A. Sen · 2017
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Approximate ultrametricity for random measures and applications to spin glasses
A. Jagannath · 2017
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Low temperature asymptotics of spherical mean field spin glasses
A. Jagannath and I. Tobasco · 2017
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The complexity of spherical p p -spin models—A second moment approach
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 the TAP free energy in the mixed p p -spin models
W.-K. Chen and D. Panchenko · 2018
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Bounds on the complexity of Replica Symmetry Breaking for spherical spin glasses
A. Jagannath and I. Tobasco · 2018
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A Gaussian small deviation inequality for convex functions
G. Paouris and P. Valettas · 2018
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On spin distributions for generic p-spin models
A. Auffinger and A. Jagannath · 2019
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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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A Morita type proof of the replica-symmetric formula for SK
E. Bolthausen · 2019
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Geometry and temperature chaos in mixed spherical spin glasses at low temperature: the perturbative regime
G. Ben Arous, E. Subag, and O. Zeitouni · 2020
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The generalized TAP free energy II
W.-K. Chen, D. Panchenko, and E. Subag · 2021
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Following the ground-states of full-RSB spherical spin glasses
E. Subag · 2021
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Convergence of the free energy for spherical spin glasses
E. Subag · 2022
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