G. Forgacs

Adsorption–desorption transition of polymer chains interacting with surfaces

We report exact results for two and three dimensional directed models of polymer chain adsorption–desorption transition in the presence of attracting substrate. A number of properties of this transition are evaluated explicitly. These include the phase diagram, the adsorption fraction and the monomer‐density profile. Our results are obtained by a novel application of the transfer matrix method particularly suitable for studies of polymer chain conformations.

Exact solution of the partially directed compact lattice animal model

The authors calculate exactly the number generating function for partially directed compact lattice animals on the square lattice. For the fully directed model, they report results of new numerical studies.

Directed Compact Lattice Animals: Exact Results

The partially directed compact lattice animal model on the square lattice is solved exactly for the cluster number and average cluster radius along the directed axis in terms of the appropriate generating functions. For the critical exponents we findθ=0 andυ‖=1. Caliper size distribution along the directed axis is also calculated analytically. It is used to confirmυ‖=1 and to study some finite-size scaling properties for this model. For the perpendicular cluster radius distribution, a combination of analytic arguments and computer results leads to a conjecture on the exact form of the appropriate generating function and to the resultυ⊥=1/2. Some calculations are reported for the triangular lattice and for hypercubic lattices ind>2.

Unbinding of semiflexible directed polymers in 1+1 dimensions

The unbinding transition of a directed semiflexible polymer whose fluctuations are controlled by bending rigidity is studied in 1+1 dimensions. The chain is modelled by a restricted solid-on-solid model with a short-ranged substrate potential. All the statistical and thermodynamic properties are evaluated exactly. In particular, the phase diagram is determined and is compared with the case when fluctuations are controlled by surface tension.

Adsorption of a directed polymer chain in the presence of monomer attraction: analytical results

The adsorption of a directed polymer chain is studied in two dimensions using a restricted solid-on-solid model and allowing for a short range attraction between monomers. All the thermodynamic properties of the chain are evaluated exactly. The system does not exhibit a collapse or chain folding transition.

Disorder-driven crossover from first-order to second-order depinning

It is shown that an extra defect line introduced into a solid-on-solid model to describe a second-order wetting transition in two dimensions may lead to a sharp first-order depinning. If disorder is introduced along the defect line, this first-order transition may be driven to second order. If the transition in the pure system is second order, disorder may drive it to first order. All the calculations leading to the above results can be performed analytically.