  In this article we study from a non-perturbative point of view the
entanglement of two directed polymers subjected to repulsive interactions given
by a Dirac $\delta-$function potential. An exact formula of the so-called
second moment of the winding angle is derived. This result is used to provide a
thorough analysis of entanglement phenomena in the classical system of two
polymers subjected to repulsive interactions and related problems. No
approximation is made in treating the constraint on the winding angle and the
repulsive forces. In particular, we investigate how repulsive forces influence
the entanglement degree of the two-polymer system. In the limit of ideal
polymers, in which the interactions are switched off, we show that our results
are in agreement with those of previous works.
