A stochastic model solvable without integrability

TL;DR

This paper introduces an exactly solvable stochastic model with diffusive and evaporation/condensation processes, revealing that mean field approximation is generally inaccurate and demonstrating asymmetry effects through analytical and numerical methods.

Contribution

The authors present a new stochastic model that can be solved exactly without relying on integrability, providing explicit correlation functions and analyzing mean field limitations.

Findings

Exact computation of all correlation functions

Mean field approximation is not generally accurate

Model exhibits asymmetry despite symmetric rates

Abstract

We introduce a model with diffusive and evaporation/condensation processes, depending on 3 parameters obeying some inequalities. The model can be solved in the sense that all correlation functions can be computed exactly without the use of integrability. We show that the mean field approximation is not exact in general. This can be shown by looking at the analytical expression of the two-point correlation functions, that we provide. We confirm our analysis by numerics based on direct diagonalisation of the Markov matrix (for small values of the number of sites) and also by Monte-Carlo simulations (for a higher number of sites). Although the model is symmetric in its diffusive rates, it exhibits a left / right asymmetry driven by the evaporation/condensation processes. We also argue that the model can be taken as a one-dimensional model for catalysis or fracturing processes.