EXISTENCE OF 4-DIMENSIONAL POLYMER COLLAPSE I - KINETIC GROWTH TRAILS

We present the results of simulations of kinetic growth trails (KGT) ( bond-avoiding walks) in four dimensions. We use a mapping from a kinet ic growth model to a static model of self-interacting trails (ISAT) at a particular temperature to argue that this temperature is precisely the collapse temperature of four-dimensional interacting trails. To do this we show that the kinetic growth trails behave neither like stati c non-interacting trails, which should behave as excluded-volume-domin ated four-dimensional polymers (that is self-avoiding walks), or colla psed four-dimensional polymers, but rather show an intermediate behavi our. This is the first indication of collapse in any four-dimensional lattice polymer model and so may be helpful in deciding which of the c ompeting models of polymers is a good model in lower dimensions. We ha ve calculated various exponents of the I(GT model and identified them with certain critical exponents of the static ISAT problem. (C) 1998 E lsevier Science B.V. All rights reserved.