# Non-integrable dimers: Universal fluctuations of tilted height profiles

## TL;DR

This paper investigates how small perturbations in non-determinantal dimer models on the square lattice affect height fluctuation amplitudes, revealing non-universal dependence on perturbations while maintaining universal scaling relations.

## Contribution

It proves that log-correlations persist in non-integrable dimer models and establishes a universal relation between fluctuation amplitude and correlation exponents.

## Key findings

- Log-correlations survive small perturbations.
- Amplitude depends non-universally on perturbation strength and tilt.
- Universal scaling relation links amplitude to correlation exponents.

## Abstract

We study a class of close-packed dimer models on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point, and the dimer model with plaquette interaction previously analyzed in \cite{A,AL,GMT17a,GMT17b}. By tuning the edge weights, we can impose a non-zero average tilt for the height function, so that the considered models are in general not symmetric under discrete rotations and reflections. In the determinantal case, height fluctuations in the massless (or `liquid') phase scale to a Gaussian log-correlated field and their amplitude is a universal constant, independent of the tilt. When the perturbation strength $\lambda$ is sufficiently small we prove, by fermionic constructive Renormalization Group methods, that log-correlations survive, with amplitude $A$ that, generically, depends non-trivially and non-universally on $\lambda$ and on the tilt. On the other hand, $A$ satisfies a universal scaling relation (`Haldane' or `Kadanoff' relation), saying that it equals the anomalous exponent of the dimer-dimer correlation.