The SK model is Full-step Replica Symmetry Breaking at zero temperature

Antonio Auffinger; Wei Kuo Chen; Qiang Zeng

The SK model is Full-step Replica Symmetry Breaking at zero temperature

Antonio Auffinger, Wei Kuo Chen, Qiang Zeng

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi’s prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.

Original language	English (US)
Journal	Unknown Journal
State	Published - Mar 20 2017

ASJC Scopus subject areas

General

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title = "The SK model is Full-step Replica Symmetry Breaking at zero temperature",

abstract = "We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi{\textquoteright}s prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.",

author = "Antonio Auffinger and Chen, {Wei Kuo} and Qiang Zeng",

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N2 - We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi’s prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.

AB - We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi’s prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.

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