# Self-avoiding trails with nearest neighbour interactions on the square lattice

*by Dr Andrea Bedini*

*Institution:*MASCOS, The University of Melbourne

*Date: Mon 15th October 2012*

*Time: 1:00 PM*

*Location: Room 115, Sidney Myer Asia Centre*

*Abstract*: 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 collapse transition of a polymer in dilute solution and, on the square lattice, it has been established numerically that their collapse transitions lie in different universality classes. The two models differ in two substantial ways: in the types of subsets of random walk configurations utilised (site self-avoidance versus bond self-avoidance) and in the type of attractive interaction. It is therefore of some interest to consider self-avoiding trails interacting via nearest neighbour attraction (INNSAT) in order to ascertain the source for the difference in the collapse universality class.