Partition function of a continuous polymer chain : a study of its anomalous behaviour in three dimensions

Abstract

Polymers in good solvents can be represented by continuous curves in a continuous space of dimension d (d = 3). In this case, all physical quantities can be expanded in powers of the interaction which can be reduced to a dimensionless parameter z. However it is shown that for d = 4 - 2/p (p = integer) the partition function of a polymer cannot be expanded in terms of z alone but has a singular double expansion in powers of z and In z. The nature and the effects of this singularity (which are apparently more formal than physical) are analysed