Abstract
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 language | English |
|---|---|
| Pages (from-to) | 691–782 |
| Number of pages | 92 |
| Journal | Communications in Mathematical Physics |
| Volume | 392 |
| Issue number | 2 |
| Early online date | 30 Mar 2022 |
| DOIs | |
| Publication status | Published - 30 Jun 2022 |
Bibliographical note
Funding Information:We thank Roman Kotecký for inspiring discussions throughout all stages of this project. We thank Nikolay Barashkov for useful discussions regarding the variational approach to ultraviolet stability for. We thank Martin Hairer for a particularly useful discussion. AC and TSG thank the Hausdorff Research Institute for Mathematics for the hospitality and support during the Fall 2019 junior trimester programme Randomness, PDEs and Nonlinear Fluctuations. AC, TSG, and HW thank the Isaac Newton Institute for Mathematical Sciences for hospitality and support during the Fall 2018 programme Scaling limits, rough paths, quantum field theory , which was supported by EPSRC Grant No. EP/R014604/1. AC was supported by the Leverhulme Trust via an Early Career Fellowship, ECF-2017-226. TSG was supported by EPSRC as part of the Statistical Applied Mathematics CDT at the University of Bath (SAMBa), Grant No. EP/L015684/1. HW was supported by the Royal Society through the University Research Fellowship UF140187 and by the Leverhulme Trust through a Philip Leverhulme Prize.
Funding Information:
We thank Roman Kotecký for inspiring discussions throughout all stages of this project. We thank Nikolay Barashkov for useful discussions regarding the variational approach to ultraviolet stability for . We thank Martin Hairer for a particularly useful discussion. AC and TSG thank the Hausdorff Research Institute for Mathematics for the hospitality and support during the Fall 2019 junior trimester programme Randomness, PDEs and Nonlinear Fluctuations. AC, TSG, and HW thank the Isaac Newton Institute for Mathematical Sciences for hospitality and support during the Fall 2018 programme Scaling limits, rough paths, quantum field theory, which was supported by EPSRC Grant No. EP/R014604/1. AC was supported by the Leverhulme Trust via an Early Career Fellowship, ECF-2017-226. TSG was supported by EPSRC as part of the Statistical Applied Mathematics CDT at the University of Bath (SAMBa), Grant No. EP/L015684/1. HW was supported by the Royal Society through the University Research Fellowship UF140187 and by the Leverhulme Trust through a Philip Leverhulme Prize.
Publisher Copyright:
© 2022, The Author(s).
Keywords
- Phase transitions
- Euclidean quantum field theory
- Singular stochastic PDEs
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics