Existence of a tricritical point for the Blume–Capel model on ℤd

Trishen Gunaratnam, Dmitrii Krachun, Christoforos Panagiotis

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Abstract

We prove the existence of a tricritical point for the Blume-Capel model on Zd for every d≥2. The proof in d≥3 relies on a novel combinatorial mapping to an Ising model on a larger graph, the techniques of Aizenman, Duminil-Copin, and Sidoravicious (Comm. Math. Phys, 2015), and the celebrated infrared bound. In d=2, the proof relies on a quantitative analysis of crossing probabilities of the dilute random cluster representation of the Blume-Capel. In particular, we develop a quadrichotomy result in the spirit of Duminil-Copin and Tassion (Moscow Math. J., 2020), which allows us to obtain a fine picture of the phase diagram in d=2, including asymptotic behaviour of correlations in all regions. Finally, we show that the techniques used to establish subcritical sharpness for the dilute random cluster model extend to any d≥2.
Original languageEnglish
Pages (from-to)785-845
Number of pages61
JournalProbability and Mathematical Physics
Volume5
Issue number3
Early online date30 Jun 2024
DOIs
Publication statusPublished - 30 Jun 2024

Keywords

  • math.PR
  • math-ph
  • math.MP
  • 60K35, 82B43

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