The spectral gap of the 2-D stochastic Ising model with mixed boundary conditions

2000/08/25 by Kenneth S. Alexander, Alexander, Kenneth S., Nobuo Yoshida +1
Mathematics · Physics and Astronomy · #60K35 (primary) #82C20 (secondary) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:60K35 #msc:82C20

paper · pdf · doi:10.48550/arxiv.math/0008201

18 pages

arxiv created 2000/08/25 · openalex publication_date 2000/08/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an n-by-n box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length n in the boundary is bounded by δn, where δ< 1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on δ), the spectral gap decreases exponentially in n.

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