Interacting growth walk on a honeycomb lattice

Abstract

The interacting growth walk (IGW) is a kinetic algorithm proposed recently for generating long, lattice polymer configurations. The growth process in IGW is tuned by a parameter called the growth temperature T G =1/( k B β G ). In this paper we consider IGW on a honeycomb lattice. We take the non-bonded nearest neighbour contact energy as ε=−1. We show that at β G =0, IGW algorithm generates a canonical ensemble of interacting self-avoiding walks at β= β ̂ (β G=0)= ln(2) . However for β G >0, IGW generates an ensemble of polymer configurations most of which are in equilibrium at β= β ̂ (β G) . The remaining ones are frozen in ‘non-equilibrium’ configurations.