The Annals of Applied Probability

Disorder chaos in some diluted spin glass models

Wei-Kuo Chen and Dmitry Panchenko

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Abstract

We prove disorder chaos at zero temperature for three types of diluted models with large connectivity parameter: $K$-spin antiferromagnetic Ising model for even $K\geq2$, $K$-spin spin glass model for even $K\geq2$, and random $K$-sat model for all $K\geq2$. We show that modifying even a small proportion of clauses results in near maximizers of the original and modified Hamiltonians being nearly orthogonal to each other with high probability. We use a standard technique of approximating diluted models by appropriate fully connected models and then apply disorder chaos results in this setting, which include both previously known results as well as new examples motivated by the random $K$-sat model.

Article information

Source
Ann. Appl. Probab., Volume 28, Number 3 (2018), 1356-1378.

Dates
Received: March 2017
First available in Project Euclid: 1 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1527840021

Digital Object Identifier
doi:10.1214/17-AAP1331

Mathematical Reviews number (MathSciNet)
MR3809466

Zentralblatt MATH identifier
06919727

Subjects
Primary: 60F10: Large deviations 60G15: Gaussian processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Keywords
Disorder chaos $p$-spin models diluted spin glasses

Citation

Chen, Wei-Kuo; Panchenko, Dmitry. Disorder chaos in some diluted spin glass models. Ann. Appl. Probab. 28 (2018), no. 3, 1356--1378. doi:10.1214/17-AAP1331. https://projecteuclid.org/euclid.aoap/1527840021


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