Fetching the paper…

Reading the bibliography…

2016

Thouless-Anderson-Palmer equations for the generic p-spin glass model

Auffinger, Antonio, Jagannath, Aukosh

Original
PDF
Post on X

Understand

We study the Thouless-Anderson-Palmer (TAP) equations for spin glasses on the hypercube.

First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, $\langle\cdot\rangle_N$, into a mixture of conditional laws, $\langle\cdot\rangle_{\alpha,N}$.
We show that the TAP equations hold for the spin at any site with respect to $\langle\cdot\rangle_{\alpha,N}$ simultaneously for all $\alpha$.
This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.

Thouless-Anderson-Palmer equations for the generic p-spin glass model · Around

Built on

Solution of ’solvable model of a spin glass’
David J Thouless, Philip W Anderson, and Robert G Palmer · 1977
Earlier work this paper cites.
Spin glasses: a challenge for mathematicians
Michel Talagrand · 2003
Earlier work this paper cites.
Random fields and geometry
Robert Adler and Jonathan Taylor · 2007
Earlier work this paper cites.
On the structure of quasi-stationary competing particle systems
Louis-Pierre Arguin and Michael Aizenman · 2009
Earlier work this paper cites.
Spin glasses and Stein’s method
Sourav Chatterjee · 2010
Earlier work this paper cites.

Similar

The Ghirlanda-Guerra identities for mixed p p -spin model
Dmitry Panchenko · 2010
Cited alongside, same era.
Construction of pure states in mean field models for spin glasses
Michel Talagrand · 2010
Cited alongside, same era.
The Parisi ultrametricity conjecture
Dmitry Panchenko · 2013
Cited alongside, same era.
The Sherrington-Kirkpatrick model
Dmitry Panchenko · 2013
Cited alongside, same era.
An iterative construction of solutions of the TAP equations for the Sherrington-Kirkpatrick model
Erwin Bolthausen · 2014
Cited alongside, same era.
Approximate Ultrametricity for Random Measures and Applications to Spin Glasses
Aukosh Jagannath
Cited in the paper.

Then

On properties of Parisi measures
Antonio Auffinger and Wei-Kuo Chen · 2015
Later among the works it cites.
The Parisi formula has a unique minimizer
Antonio Auffinger and Wei-Kuo Chen · 2015
Later among the works it cites.
Hierarchical exchangeability of pure states in mean field spin glass models
Dmitry Panchenko · 2015
Later among the works it cites.
On spin distributions for generic p p -spin models
Antonio Auffinger and Aukosh Jagannath · 2018
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…