Overlap properties and adsorption transition of two Hamiltonian paths

Details Overlap properties and adsorption transition of two Hamiltonian paths Overlap properties and adsorption transition of two Hamiltonian paths

1998-12-03

arxiv.org/abs/cond-mat/9812059v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, 2 figures

Scientific paper

10.1007/s100510050957

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. Using a ($n=0$ component) spin representation for these paths, we show the existence of a phase transition for strong coupling (i.e. at low temperature) 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 particuliar that two HP with overlap greater than $q_M$ coincide. These results may be of interest in (bio)polymers and in optimization problems.

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