FK–Ising coupling applied to near-critical planar models

Federico Camia, Jianping Jiang*, Charles M. Newman

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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
Pages (from-to)560-583
Number of pages24
JournalStochastic Processes and Their Applications
Issue number2
Early online date11 Feb 2019
Publication statusPublished - 1 Feb 2020


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


Dive into the research topics of 'FK–Ising coupling applied to near-critical planar models'. Together they form a unique fingerprint.

Cite this