Collapse transition of directed polymers: Exact results

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Abstract
The phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive substrate and monomer-monomer interactions has been calculated exactly using transfer-matrix techniques. It is shown that the first-order transition line separating the collapsed and bound phases ends up in a multicritical point, while the transition temperature for the extended-collapsed transition is independent of the adsorption potential. The crossover exponent at the FTHETA point is found to be Φ=1/3.