POLYMER-CHAIN IN A RANDOM ARRAY OF TOPOLOGICAL OBSTACLES - CLASSIFICATION AND STATISTICS OF COMPLEX LOOPS

An arbitrary complex polymer loop embedded in three-dimensional space and topologically entangled with a quenched array of randomly dstribut ed parallel rods is considered. It is shown that an ensemble of the co mplex loops, prepared in different possible ways, is equivalent to the ensemble of cactuslike graphs where the leaves of these cacti are sim ple loops. The free energy of the cactuslike graphs is calculated in t he mean-field approximation. The critical condition for the collapse t ransition is obtained. The collapsed state of the complex loop with th e density distributed over different leaves is shown to be preferable.