Eur. Phys. J. B 11, 463-468 (1999)
https://doi.org/10.1007/s100510050957

Overlap properties and adsorption transition of two Hamiltonian paths

¹ Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, P.O. Box 563, 34100 Trieste, Italy
² Service de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France

Received: 4 December 1998
Revised: 10 March 1999
Published online: 15 October 1999

Abstract

We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. We use a (n=0 component) spin representation for these paths, and we evaluate the resulting partition function within a homogeneous saddle point approximation. For strong coupling (i.e. at low temperature), one finds a phase transition towards a "frozen" phase where one chain is completely adsorbed onto the other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds between two HP, i.e. their overlap q, has both lower (q_m) and upper (q_M) bounds. This means in particular that two HP with overlap greater than q_M coincide. These results may be of interest in (bio)polymers and in optimization problems.