Existence of four-dimensional polymer collapse I. Kinetic growth trails
نویسندگان
چکیده
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 selfinteracting 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 excludedvolume-dominated four-dimensional polymers (that is self-avoiding walks), or collapsed fourdimensional polymers, but rather show an intermediate behaviour. This is the rst 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 identi ed them with certain critical exponents of the static ISAT problem. c © 1998 Elsevier Science B.V. All rights reserved. PACS: 05.50.+q; 61.41.+e; 05.70.Fh
منابع مشابه
Anomalous critical behavior in the polymer collapse transition of three-dimensional lattice trails.
Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently a two-dimensional model (triangular lattice) where doubly and triply visited sites are given different weights was shown to display a rich phase diagram with first- and second-order collapse separa...
متن کاملCollapse transition of self-avoiding trails on the square lattice
The collapse transition of an isolated polymer has been modelled by many different approaches, including lattice models based on self-avoiding walks and self-avoiding trails. In two dimensions, previous simulations of kinetic growth trails, which map to a particular temperature of interacting self-avoiding trails, showed markedly different behaviour for what was argued to be the collapse transi...
متن کاملAnomalous critical behaviour in the polymer collapse transition of three-dimensional lattice trails
Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently, a two-dimensional model (triangular lattice) where doubly and triply visited sites are given different weights was shown to display a rich phase diagram with first and second order collapse separa...
متن کاملFour-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 temperatures up to length 4096 and at some temperatures up to length 16384. The results confirm the earlier prediction (using data from a non-standard model at a single temperature) of a collapse phase transition occurring at finite temperature. More...
متن کاملSelf-avoiding trails with nearest-neighbour interactions on the square lattice
Self-avoiding walks and self-avoiding trails, two models of a polymer coil in dilute solution, have been shown to be governed by the same universality class. On the other hand, self-avoiding walks interacting via nearest-neighbour contacts (ISAW) and self-avoiding trails interacting via multiply visited sites (ISAT) are two models of the coil-globule, or collapse transition of a polymer in dilu...
متن کامل