Existence of four-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 kinetic 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 static non-interacting trails, which should behave as excluded-volume-dominated four-dimensional polymers (that is self-avoiding walks), or collapsed four-dimensional polymers, but rather show an intermediate behaviour. This is the first indication of collapse in any four-dimensional lattice polymer model and so may be helpful in deciding which of the competing models of polymers is a good model in lower dimensions. We have calculated various exponents of the KGT model and identified them with certain critical exponents of the static ISAT problem.