Universal critical properties of the Eulerian bond-cubic model

TL;DR

This study uses Monte Carlo simulations to analyze the critical properties of the Eulerian bond-cubic model on a square lattice, confirming theoretical predictions and revealing differences at specific parameter values.

Contribution

It provides the first numerical estimates of two fractal dimensions and clarifies the role of cubic anisotropy at different n values.

Findings

Two fractal dimensions obtained for the first time.

Results align with Coulomb gas predictions for n<2.

Cubic anisotropy is marginal at n=2 and irrelevant for n<2.

Abstract

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of $n$. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O($n$) branch for $n < 2$ and the results obtained by previous transfer matrix calculations. For $n=2$, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model. These results confirm that the cubic anisotropy is marginal at $n=2$ but irrelevant for $n<2$.