Interacting Growth Walk on a honeycomb lattice

The Interacting Growth Walk (IGW) is a kinetic algorithm proposed recently for generating long, compact, self avoiding walks. The growth process in IGW is tuned by the so called growth temperature $T' = 1/(k_B \beta ')$. On a square lattice and at $T' = 0$, IGW is attrition free and hence grows indefinitely. In this paper we consider IGW on a honeycomb lattice. We take contact energy, see text, as $\epsilon=-|\epsilon|=-1$. We show that IGW at $\beta' =\infty$ ($T'=0$) is identical to Interacting Self Avoiding Walk (ISAW) at $\beta=\ln 4$ ($k_B T = 1/\ln 4=0.7213$). Also IGW at $\beta ' = 0$ ($T' = \infty$) corresponds to ISAW at $\beta = \ln 2$ ($k_B T= 1/ln 2 = 1.4427$). For other temperatures we need to introduce a statistical weight factor to a walk of the IGW ensemble to make correspondence with the ISAW ensemble.