Nonlocal Asymmetric exclusion process on a ring and conformal invariance

TL;DR

This paper introduces a nonlocal exclusion process on a ring, explores its phase diagram and current behavior, and identifies a conformal invariant case at specific parameters, supported by Monte Carlo simulations.

Contribution

It presents a novel nonlocal hopping model related to growth processes, analyzes its phase diagram, and conjectures an exact current value at conformal invariance.

Findings

Conformal invariance occurs at half-filling and u=1.

Exact current value is conjectured and verified for large systems.

Current exhibits non-analytic behavior near half-filling for u > 1.

Abstract

We present a one-dimensional nonlocal hopping model with exclusion on a ring. The model is related to the Raise and Peel growth model. A nonnegative parameter $u$ controls the ratio of the local backwards and nonlocal forwards hopping rates. The phase diagram and consequently the values of the current, depend on $u$ and the density of particles. In the special case of half-filling and $u = 1$ the system is conformal invariant and an exact value of the current for any size $L$ of the system is conjectured and checked for large lattice sizes in Monte Carlo simulations. For $u > 1$ the current has a non-analytic dependence on the density when the latter approaches the half-filling value.