Exactly solvable model of A + A \to 0 reactions on a heterogeneous catalytic chain

TL;DR

This paper provides an exact solution for the equilibrium properties of a one-dimensional catalytic A + A → 0 reaction model with various distributions of catalytic sites, revealing detailed insights into the system's behavior.

Contribution

It introduces an exact analytical solution for a 1D catalytic reaction model with different site distributions, expanding understanding of disorder effects in such systems.

Findings

Derived exact expressions for disorder-averaged pressure.

Obtained asymptotic mean particle density expressions.

Extended the class of exactly solvable 1D Ising-type models.

Abstract

We present an exact solution describing equilibrium properties of the catalytically-activated A + A \to 0 reaction taking place on a one-dimensional lattice, where some of the sites possess special "catalytic" properties. The A particles undergo continuous exchanges with the vapor phase; two neighboring adsorbed As react when at least one of them resides on a catalytic site (CS). We consider three situations for the CS distribution: regular, annealed random and quenched random. For all three CS distribution types, we derive exact results for the disorder-averaged pressure and present exact asymptotic expressions for the particles' mean density. The model studied here furnishes another example of a 1D Ising-type system with random multi-site interactions which admits an exact solution.