Four-dimensional polymer collapse II: interacting self-avoiding trails

We have simulated four-dimensional interacting self-avoiding trails (ISAT) on the hypercubic lattice with standard interactions at a wide range of tem peratures up to length 4096 and at some temperatures up to length 16384. Th e results confirm the earlier prediction (using data from a non-standard mo del at a single temperature) of a collapse phase transition occurring at fi nite temperature. Moreover they are in accord with the phenomenological the ory originally proposed by Lifshitz, Grosberg and Khokhlov in three dimensi ons and recently given new impetus by its use in the description of simutat ional results for four-dimensional interacting self-avoiding walks (ISAW). In fact, we argue that the available data is consistent with the conclusion that the collapse transitions of ISAT and ISAW lie in the same universalit y class, in contradiction with long-standing predictions. We deduce that th ere exists a pseudo-first order transition for ISAT in four dimensions at f inite lengths while the thermodynamic limit is described by the standard po lymer mean-field theory (giving a second-order transition), in contradictio n to the prediction that the upper critical dimension for ISAT is d(u) = 4. (C) 2001 Elsevier Science B.V. All rights reserved.