15 June 2023 Correlation length of the two-dimensional random field Ising model via greedy lattice animal
Jian Ding, Mateo Wirth
Author Affiliations +
Duke Math. J. 172(9): 1781-1811 (15 June 2023). DOI: 10.1215/00127094-2022-0077

Abstract

For the two-dimensional random field Ising model where the random field is given by independent and identically distributed mean zero Gaussian variables with variance ε2, we study (one natural notion of) the correlation length, which is the critical size of a box at which the influences of the random field and of the boundary condition on the spin magnetization are comparable. We show that as ε0, at zero temperature the correlation length scales as eΘ(ε43) (and our upper bound applies for all positive temperatures).

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Jian Ding. Mateo Wirth. "Correlation length of the two-dimensional random field Ising model via greedy lattice animal." Duke Math. J. 172 (9) 1781 - 1811, 15 June 2023. https://doi.org/10.1215/00127094-2022-0077

Information

Received: 10 January 2021; Revised: 22 June 2022; Published: 15 June 2023
First available in Project Euclid: 4 May 2023

MathSciNet: MR4608331
zbMATH: 07714224
zbMATH: 1536.60092
Digital Object Identifier: 10.1215/00127094-2022-0077

Subjects:
Primary: 60K35

Keywords: correlation length , greedy lattice animal , random field Ising model

Rights: Copyright © 2023 Duke University Press

Vol.172 • No. 9 • 15 June 2023
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