Six-vertex model and Schramm-Loewner evolution.
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Kenyon, Richard
Miller, Jason
Sheffield, Scott
Wilson, David B
Abstract
Square ice is a statistical mechanics model for two-dimensional ice, widely believed to have a conformally invariant scaling limit. We associate a Peano (space-filling) curve to a square ice configuration, and more generally to a so-called six-vertex model configuration, and argue that its scaling limit is a space-filling version of the random fractal curve SLE_{κ}, Schramm-Loewner evolution with parameter κ, where 4<κ≤12+8sqrt[2]. For square ice, κ=12. At the "free-fermion point" of the six-vertex model, κ=8+4sqrt[3]. These unusual values lie outside the classical interval 2≤κ≤8.
Description
Keywords
4902 Mathematical Physics, 51 Physical Sciences, 49 Mathematical Sciences, 5103 Classical Physics
Journal Title
Phys Rev E
Conference Name
Journal ISSN
2470-0045
2470-0053
2470-0053
Volume Title
95
Publisher
American Physical Society (APS)
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/I03372X/1)
Engineering and Physical Sciences Research Council (EP/K032208/1)
Engineering and Physical Sciences Research Council (EP/L018896/1)
Engineering and Physical Sciences Research Council (EP/K032208/1)
Engineering and Physical Sciences Research Council (EP/L018896/1)