A heterogeneous zero-range process related to a two-dimensional walk model

TL;DR

This paper explores a disordered driven-diffusive system mapped onto a heterogeneous zero-range process, revealing exact partition functions via matrix product formalism and linking it to a two-dimensional walk model.

Contribution

It introduces a novel connection between a disordered driven-diffusive system and a two-dimensional walk model through a heterogeneous zero-range process, with exact partition function calculations.

Findings

Exact grand-canonical partition function derived

Partition function of the walk model shown to be equivalent

Canonical partition function explicitly calculated

Abstract

We have considered a disordered driven-diffusive system defined on a ring. This system can be mapped onto a heterogeneous zero-range process. We have shown that the grand-canonical partition function of this process can be obtained using a matrix product formalism and that it is exactly equal to the partition function of a two-dimensional walk model. The canonical partition function of this process is also calculated. Two simple examples are presented in order to confirm the results.