Exactly solvable model of reactions on a random catalytic chain

TL;DR

This paper presents an exact solution for a one-dimensional catalytic reaction model with different spatial arrangements of catalytic sites, providing insights into particle density and system pressure in a random lattice setting.

Contribution

It introduces an exactly solvable 1D reaction model with random and regular catalytic site distributions, extending understanding of Ising-type systems with multisite interactions.

Findings

Exact partition function derived for all site arrangements.

Asymptotic expressions for particle density and compressibility.

Model exemplifies a solvable 1D system with random multisite interactions.

Abstract

In this paper we study a catalytically-activated A + A \to 0 reaction taking place on a one-dimensional regular lattice which is brought in contact with a reservoir of A particles. The A particles have a hard-core and undergo continuous exchanges with the reservoir, adsorbing onto the lattice or desorbing back to the reservoir. Some lattice sites possess special, catalytic properties, which induce an immediate reaction between two neighboring A particles as soon as at least one of them lands onto a catalytic site. We consider three situations for the spatial placement of the catalytic sites: regular, annealed random and quenched random. For all these cases we derive exact results for the partition function, and the disorder-averaged pressure per lattice site. We also present exact asymptotic results for the particles' mean density and the system's compressibility. The model studied here furnishes another example of a 1D Ising-type system with random multisite interactions which admits an exact solution.