Collapsing and adsorbing polygons

The adsorption transition in the phase diagram of a self-interacting lattice polygon is examined. The polygon has a nearest-neighbour contact fugacity and the interaction between the polygon and an impenetrable wall is modelled by a visit fugacity which is conjugate to the number of vertices of the polygon incident with the wall. The partition function of this model is Z C.y;z/D P v;cp C.v;c/y v z c , where p C.v;c/ is the number of polygons with c nearest- neighbour contacts, v visits to the wall, and n edges (and counted up to translations parallel to the wall). The limiting free energy of this model is F C.y;z/ D limn!1 1 logZ C.y;z/, and it is known to be a non-analytic function of y for each z 1 for all z2.0;1/.

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