Limit shapes for the dimer model

2017/12/22 by Kuchumov, Nikolai
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1712.08396

Abstract

We prove the existence of a limit shape for the dimer model on planar periodic bipartite graphs with an arbitrary fundamental domain and arbitrary periodic weights. This proof is based on a variational principle that uses the locality of the model and the compactness of the space of states.

Related

• Dimers and M-Curves: Limit Shapes from Riemann Surfaces
• The multinomial dimer model
• Lectures on Dimers
• Dimers on Riemann surfaces and compactified free field
• Dimer model, bead model and standard Young tableaux: finite cases and limit shapes