Topological frustration and quasicompact phase in a model of interacting polymers

Abstract

The authors study the geometric and thermal properties of a model of self-interacting linear polymers (self-avoiding walks) on a fractal lattice, the three-dimensional modified Sierpinski gasket of base b=3. As a consequence of the topological structure of this lattice, the polymer is 'frustrated' and cannot fill the available space with a finite density. When strong attractive interactions between monomers are present the polymer cannot reach the compact globule state usually observed. Rather, it shrinks into a novel phase, the 'semicompact' state, below a finite critical temperature. In this phase, the monomer density per lattice site vanishes asymptotically for large polymers. The authors give the exact values of the critical exponents at this transition and discuss its possible relevance for polymers placed in a random matrix.