FK–Ising coupling applied to near-critical planar models

Federico Camia, Jianping Jiang, Charles Newman

Research output: Contribution to journalArticle

Abstract

We consider the Ising model at its critical temperature with external magnetic field ha 15∕8 on aZ 2 . 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 Z 2 satisfies M(h)∕h 1∕15 → some B∈(0,∞) as h↓0.

Original languageEnglish (US)
JournalStochastic Processes and their Applications
DOIs
StatePublished - Jan 1 2019

Fingerprint

Reflection Positivity
Ising model
Continuum Limit
Correlation Length
Critical Temperature
Magnetization
Ising Model
External Field
Tail
Magnetic Field
Exponent
Magnetic fields
Upper bound
Estimate
Temperature
Model

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

Cite this

FK–Ising coupling applied to near-critical planar models. / Camia, Federico; Jiang, Jianping; Newman, Charles.

In: Stochastic Processes and their Applications, 01.01.2019.

Research output: Contribution to journalArticle

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