# Mass condensation in one dimension with pair-factorized steady states

## TL;DR

This paper studies mass transport models on a one-dimensional ring, analyzing phase transitions to condensation, characterizing condensate shapes, and exploring how local interactions influence static properties, supported by analytical and numerical methods.

## Contribution

It introduces a detailed analysis of condensation phenomena in one-dimensional mass transport models with pair-factorized steady states, including shape and scaling of condensates.

## Key findings

- Condensation transition depends on weight functions and interactions.
- Condensate shape varies from delta-like to rectangular based on parameters.
- Analytical predictions align well with numerical simulations.

## Abstract

We consider stochastic rules of mass transport which lead to steady states that factorize over the links of a one-dimensional ring. Based on the knowledge of the steady states, we derive the onset of a phase transition from a liquid to a condensed phase that is characterized by the existence of a condensate. For various types of weight functions which enter the hopping rates, we determine the shape of the condensate, its scaling with the system size, and the single-site mass distribution as characteristic static properties. As it turns out, the condensate's shape and its scaling are not universal, but depend on the competition between local and ultralocal interactions. So we can tune the shape from a delta-like envelope to a parabolic-like or a rectangular one. While we treat the liquid phase in the grand-canonical formalism, we develop a different analytical approach for the condensed phase. Its predictions are well confirmed by numerical simulations. Possible extensions to higher dimensions are indicated.