Work

Scaling limit of domino tilings on a pentagonal domain

Year: 2024

Type: article

Abstract: We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular nonlocal correlation function, essentially equivalent to the partition function for the domino tilings of a pentagon-shaped domain, obtained by cutting away a triangular region from a corner of the initial Aztec diamond. We observe a third-order phase transition when the geometric parameters of the obtained pentagonal domain are tuned to have the fifth side exactly tangent to the arctic ellipse of the corresponding initial model.

Source: Physical review. E

DOI: 10.1103/physreve.110.054140

Authors: Filippo Colomo, Andrei G. Pronko

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Steklov Mathematical Institute

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Ministry of Education and Science of the Russian Federation, Foundation for the Advancement of Theoretical Physics and Mathematics

Awards: Institute for Pure and Applied Mathematics, G3949099953, G8105343478