Non-integrable dimer models: universality and scaling relations
arXiv:1905.04011 · doi:10.1063/1.5109618
Abstract
In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including: weakly non-integrable 2D Ising models, Ashkin-Teller, 8-Vertex, and close-packed interacting dimer models. In this note, we will focus on the illustrative example of the interacting dimer model and review some of the universality results derived in this context. In particular, we will discuss the massless Gaussian free field (GFF) behavior of the height fluctuations. It turns out that GFF behavior is connected with a remarkable identity (`Haldane' or 'Kadanoff relation') between an amplitude and an anomalous critical exponent, characterizing the large distance behavior of the dimer-dimer correlations.
arXiv commentto appear on J. Math. Phys., special volume dedicated to the ICMP 2018. 23 pages, 3 figures
References in corpus (17)
- The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
- Local statistics of lattice dimers
- Interacting classical dimers on the square lattice
- Classical dimers with aligning interactions on the square lattice
- Height fluctuations in interacting dimers
- 2D models of statistical physics with continuous symmetry: the case of singular interactions
- Anomalous universality in the anisotropic Ashkin-Teller model
- Fluctuations for the Ginzburg-Landau Interface Model on a Bounded Domain
- Universal Relations for Non Solvable Statistical Models
- Extended scaling relations for planar lattice models
- Delocalization of two-dimensional random surfaces with hard-core constraints
- Universality relations in non-solvable quantum spin chains
- Emergent Planarity in two-dimensional Ising Models with finite-range Interactions
- Anomalous critical exponents in the anisotropic Ashkin-Teller model
- Haldane relation for interacting dimers
- Drude weight in non solvable quantum spin chains
- Integrability as a consequence of discrete holomorphicity: loop models