Phase transitions for ϕ43
File(s)Chandra2022_Article_PhaseTransitionsForPhi43Φ34.pdf (1.36 MB)
Published version
Author(s)
Chandra, Ajay
Gunaratnam, Trishen S
Weber, Hendrik
Type
Journal Article
Abstract
We establish a surface order large deviation estimate for the magnetisation of low temperature ϕ43. As a byproduct, we obtain a decay of spectral gap for its Glauber dynamics given by the ϕ43 singular stochastic PDE. Our main technical contributions are contour bounds for ϕ43, 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 ϕ43 whilst preserving the structure of the low temperature potential. To do this, we build on the variational approach to ultraviolet stability for ϕ43 developed recently by Barashkov and Gubinelli (Duke Math. J. 169(17):3339–3415, 2020).
Date Issued
2022-03-30
Date Acceptance
2022-02-18
Citation
Communications in Mathematical Physics, 2022, 392, pp.691-782
ISSN
0010-3616
Publisher
Springer Science and Business Media LLC
Start Page
691
End Page
782
Journal / Book Title
Communications in Mathematical Physics
Volume
392
Copyright Statement
© The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://link.springer.com/article/10.1007/s00220-022-04353-6
Subjects
Science & Technology
Physical Sciences
Physics, Mathematical
Physics
MEAN FIELD-THEORY
LARGE DEVIATIONS
LATTICE APPROXIMATION
CONVERGENT EXPANSION
MASS GAP
MODEL
EQUILIBRIUM
TRIVIALITY
POSITIVITY
CRYSTAL
Mathematical Physics
0101 Pure Mathematics
0105 Mathematical Physics
0206 Quantum Physics
Publication Status
Published
Date Publish Online
2022-03-30