Exactly Solvable Model of Monomer-Monomer Reactions on a Two-Dimensional Random Catalytic Substrate

G. Oshanin, M. N. Popescu, and S. Dietrich

Phys. Rev. Lett. 93, 020602 – Published 8 July 2004

Abstract

We study the equilibrium properties of a monomer-monomer $A + B \to \emptyset︀$ reaction on a two-dimensional substrate containing randomly placed catalytic bonds. Interacting $A$ and $B$ species undergo continuous exchanges with particle reservoirs and react as soon as a pair of unlike particles appears on sites connected by a catalytic bond. For annealed disorder in the placement of catalytic bonds the model is mapped onto a general spin $S = 1$ model and solved exactly for the pressure in a particular case. At equal activities of the two species a second order phase transition is revealed.

Received 26 November 2003

DOI:https://doi.org/10.1103/PhysRevLett.93.020602

Authors & Affiliations

G. Oshanin^1,2,3,*, M. N. Popescu^2,3,†, and S. Dietrich^2,3,‡

¹Laboratoire de Physique Théorique des Liquides, Université Paris 6, 4 Place Jussieu, 75252 Paris, France
²Max-Planck-Institut für Metallforschung, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
³Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

^*Electronic address: oshanin@lptl.jussieu.fr
^†Electronic address: popescu@mf.mpg.de
^‡Electronic address: dietrich@mf.mpg.de

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Vol. 93, Iss. 2 — 9 July 2004

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