Phase transitions for φ43

Ajay Chandra, Trishen S. Gunaratnam, Hendrik Weber

Research output: Contribution to journalArticlepeer-review


We establish a surface order large deviation estimate for the magnetisation of low temperature ϕ34. As a byproduct, we obtain a decay of spectral gap for its Glauber dynamics given by the ϕ34 singular stochastic PDE. Our main technical contributions are contour bounds for ϕ34, which extends 2D results by Glimm et al. (Commun Math Phys 45(3):203–216, 1975). We adapt an argument by Bodineau et al. (J Math Phys 41(3):1033–1098, 2000) to use these contour bounds to study phase segregation. The main challenge to obtain the contour bounds is to handle the ultraviolet divergences of ϕ34 whilst preserving the structure of the low temperature potential. To do this, we build on the variational approach to ultraviolet stability for ϕ34 developed recently by Barashkov and Gubinelli (Duke Math. J. 169(17):3339–3415, 2020).

Original languageEnglish
Pages (from-to)691–782
Number of pages92
JournalCommunications in Mathematical Physics
Issue number2
Early online date30 Mar 2022
Publication statusPublished - 30 Jun 2022


  • Phase transitions
  • Euclidean quantum field theory
  • Singular stochastic PDEs

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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