On properties of the spherical mixed vector p-spin model

Antonio Auffinger; Yuxin Zhou

doi:10.1016/j.spa.2022.02.001

On properties of the spherical mixed vector p-spin model

Antonio Auffinger^*, Yuxin Zhou

^*Corresponding author for this work

Mathematics

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

Abstract

This paper studies properties of the mixed spherical vector p-spin model. At zero temperature, we establish and investigate a Parisi type formula for the ground state energy. At finite temperature, we provide some properties of minimizers of the Crisanti–Sommers formula recently obtained in Ko (2018). In particular, we extend some of the one-dimensional Parisi measure results of Auffinger and Chen (2015) to the vector case.

Original language	English (US)
Pages (from-to)	382-413
Number of pages	32
Journal	Stochastic Processes and their Applications
Volume	146
DOIs	https://doi.org/10.1016/j.spa.2022.02.001
State	Published - Apr 2022

Keywords

Crisanti–Sommers
Ground state energy
Parisi's formula
Spherical vector p-spin
Spin glass

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Access to Document

10.1016/j.spa.2022.02.001

Cite this

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title = "On properties of the spherical mixed vector p-spin model",

abstract = "This paper studies properties of the mixed spherical vector p-spin model. At zero temperature, we establish and investigate a Parisi type formula for the ground state energy. At finite temperature, we provide some properties of minimizers of the Crisanti–Sommers formula recently obtained in Ko (2018). In particular, we extend some of the one-dimensional Parisi measure results of Auffinger and Chen (2015) to the vector case.",

keywords = "Crisanti–Sommers, Ground state energy, Parisi's formula, Spherical vector p-spin, Spin glass",

author = "Antonio Auffinger and Yuxin Zhou",

note = "Funding Information: Research partially supported by National Science Foundation, United States of America Grant CAREER DMS-1653552, Simons Foundation/SFARI, United States of America (597491-RWC), and National Science Foundation Grant 1764421. Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

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AU - Zhou, Yuxin

N1 - Funding Information: Research partially supported by National Science Foundation, United States of America Grant CAREER DMS-1653552, Simons Foundation/SFARI, United States of America (597491-RWC), and National Science Foundation Grant 1764421. Publisher Copyright: © 2022 Elsevier B.V.

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N2 - This paper studies properties of the mixed spherical vector p-spin model. At zero temperature, we establish and investigate a Parisi type formula for the ground state energy. At finite temperature, we provide some properties of minimizers of the Crisanti–Sommers formula recently obtained in Ko (2018). In particular, we extend some of the one-dimensional Parisi measure results of Auffinger and Chen (2015) to the vector case.

AB - This paper studies properties of the mixed spherical vector p-spin model. At zero temperature, we establish and investigate a Parisi type formula for the ground state energy. At finite temperature, we provide some properties of minimizers of the Crisanti–Sommers formula recently obtained in Ko (2018). In particular, we extend some of the one-dimensional Parisi measure results of Auffinger and Chen (2015) to the vector case.

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KW - Ground state energy

KW - Parisi's formula

KW - Spherical vector p-spin

KW - Spin glass

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