COLLAPSE OF A POLYMER IN 2 DIMENSIONS

We numerically investigate the influence of self-attraction on the cri tical behaviour of a polymer in two dimensions, by means of an analysi s of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the basis of the O(n) loop model in the limi t n --> 0. It yields finite-size results for the magnetic correlation length of systems with a cylindrical geometry. A comparison with the p redictions of finite-size scaling enables us to obtain information abo ut the phase diagram as a function of the chemical potential of the lo op segments and the strength of the attractive potential. Results for the magnetic scaling dimension can be interpreted in terms of known un iversality classes. In particular, when the attractive potential is in creased, we observe the crossover between the polymer critical behavio ur of the self-avoiding walk type to behaviour described earlier for t he theta point. (C) 1998 Elsevier Science B.V. All rights reserved.