Exact Solution of the Asymmetric Exclusion Model with Particles of Arbitrary Size

TL;DR

This paper introduces an exact solution for a generalized asymmetric exclusion model with particles of arbitrary sizes, revealing that its critical behavior aligns with the KPZ universality class.

Contribution

It extends the asymmetric exclusion model to include particles of various sizes and solves it exactly using Bethe ansatz, connecting it to surface growth phenomena.

Findings

Model solved exactly via Bethe ansatz

Dynamical critical exponent z calculated

Model exhibits KPZ universality class behavior

Abstract

A generalization of the simple exclusion asymmetric model is introduced. In this model an arbitrary mixture of molecules with distinct sizes $s = 0,1,2,...$, in units of lattice space, diffuses asymmetrically on the lattice. A related surface growth model is also presented. Variations of the distribution of molecules's sizes may change the excluded volume almost continuously. We solve the model exactly through the Bethe ansatz and the dynamical critical exponent $z$ is calculated from the finite-size corrections of the mass gap of the related quantum chain. Our results show that for an arbitrary distribution of molecules the dynamical critical behavior is on the Kardar-Parizi-Zhang (KPZ) universality.