Connection probabilities of multiple FK-Ising interfaces

Yu Feng, Eveliina Peltola, Hao Wu*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
12 Downloads (Pure)

Abstract

We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight q∈[1,4). Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are beyond reach for other values of q than the FK-Ising model (q=2). Given the convergence of interfaces, the conjectural formulas for other values of q could be verified similarly with relatively minor technical work. The limit interfaces are variants of SLEκ curves (with κ=16/3 for q=2). Their partition functions, that give the connection probabilities, also satisfy properties predicted for correlation functions in conformal field theory (CFT), expected to describe scaling limits of critical random-cluster models. We verify these properties for all q∈[1,4), thus providing further evidence of the expected CFT description of these models.

Original languageEnglish
Pages (from-to)281-367
Number of pages87
JournalProbability Theory and Related Fields
Volume189
Issue number1-2
DOIs
Publication statusPublished - Jun 2024
MoE publication typeA1 Journal article-refereed

Keywords

  • 60J67
  • 60K35
  • 82B20
  • Conformal field theory
  • Correlation function
  • Crossing probability
  • FK-Ising model
  • Partition function
  • Random-cluster model
  • Schramm–Loewner evolution

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