Non-intersection exponents of fully packed trails on the square lattice

TL;DR

This paper numerically investigates the non-intersection exponents of fully packed trails on the square lattice, revealing results consistent with conformal field theory predictions similar to Brownian motion, but with subtle differences.

Contribution

It provides the first numerical evidence that non-intersection exponents of fully packed trails align with CFT formulas akin to Brownian motion, with observed slight variations.

Findings

Non-intersection exponents match CFT formulas similar to Brownian motion

Evidence suggests slight differences in exponents compared to Brownian case

Numerical methods include transfer matrix and Monte Carlo simulations

Abstract

Fully packed trails on the square lattice are known to be described, in the long distance limit, by a collection of free non compact bosons and symplectic fermions, and thus exhibit some properties reminiscent of Brownian motion, like vanishing fuseau exponents. We investigate in this paper the situation for their non-intersection exponents. Our approach is purely numerical, and based both on transfer matrix and Monte Carlo calculations. We find some evidence for non-intersection exponents given by CFT formulas similar to the Brownian case, albeit slightly different in their details.