Collapse of a polymer in two dimensions

Details Collapse of a polymer in two dimensions Collapse of a polymer in two dimensions

1997-09-26

arxiv.org/abs/cond-mat/9709290v1

Physica A, 251 (1998) 95-103

Physics

Condensed Matter

Statistical Mechanics

11 pages, Latex, 3 eps figs, Elsevier style files, to appear in the Hans van Leeuwen Festschrift (Physica A)

Scientific paper

We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the basis of the O($n$) loop model in the limit $n \to 0$. It yields finite-size results for the magnetic correlation length of systems with a cylindrical geometry. A comparison with the predictions of finite-size scaling enables us to obtain information about the phase diagram as a function of the chemical potential of the loop segments and the strength of the attractive potential. Results for the magnetic scaling dimension can be interpreted in terms of known universality classes. In particular, when the attractive potential is increased, we observe the crossover between polymer critical behaviour of the self-avoiding walk type to behaviour described earlier for the theta point.

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