FK–Ising coupling applied to near-critical planar models

Federico Camia, Jianping Jiang and Charles M. Newman

Stochastic Processes and their Applications, 2020, vol. 130, issue 2, 560-583

Abstract: We consider the Ising model at its critical temperature with external magnetic field ha15∕8 on aZ2. We give a purely probabilistic proof, using FK methods rather than reflection positivity, that for a=1, the correlation length is ≥const.h−8∕15 as h↓0. We extend to the a↓0 continuum limit the FK–Ising coupling for all h>0, and obtain tail estimates for the largest renormalized cluster area in a finite domain as well as an upper bound with exponent 1∕8 for the one-arm event. Finally, we show that for a=1, the average magnetization, M(h), in Z2 satisfies M(h)∕h1∕15→ some B∈(0,∞) as h↓0.

Keywords: Ising model; Magnetization field; Near-critical; Correlation length; Exponential decay; Magnetization exponent; FK-Ising coupling (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.02.003

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