FK–Ising coupling applied to near-critical planar models

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)560-583
Number of pages24
JournalStochastic Processes and their Applications
Volume130
Issue number2
DOIs
StatePublished - Feb 2020

Keywords

  • Correlation length
  • Exponential decay
  • FK-Ising coupling
  • Ising model
  • Magnetization exponent
  • Magnetization field
  • Near-critical

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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