  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.

Condensed Matter