CRITICAL BEHAVIOUR OF FRUSTRATED WALKS ON THE SQUARE LATTICE

Damien Foster (Personal webpage)

In this talk I will present a range of 2D lattice models for polymers in dilute solution which do not display the Universality properties one might naively expect. I will argue that this is due to frustration effects with the underlying lattice.

After initially reviewing the standard model for polymers in solution (the Theta point model) I will proceed to introduce the transfer matrix method and its extensions (CTMRG and DMRG) to deal with these methods. I will discuss the critical behaviour observed and some outstanding questions.

I will finish the talk by discussing the use of growth Monte Carlo methods to look at the high-temperature series expansions for these models, and investigate the behaviour of the partition function zeros. The details of evaporation-driven self-assembly and stratification of the sticks in the vertical direction are discussed.