# Non-integrable dimer models: universality and scaling relations

## TL;DR

This paper reviews the application of Fermionic Renormalization Group methods to non-integrable dimer models, highlighting universality and scaling relations, especially the connection between height fluctuations and critical exponents.

## Contribution

It demonstrates the universality of scaling limits in non-integrable dimer models and elucidates the relation between amplitude and critical exponents via the GFF behavior.

## Key findings

- GFF behavior of height fluctuations in dimer models
- Universal scaling relations and amplitude-exponent identities
- Application of Fermionic RG methods to non-integrable models

## 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.