Interacting Growth Walk on a honeycomb lattice

Abstract

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 $T^{\prime }=1/(k_B{\beta }^{\prime })$. On a square lattice and at $T^{\prime }=0$, 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 ${\beta }^{\prime }=\infty$ ($T^{\prime }=0$) is identical to Interacting Self Avoiding Walk (ISAW) at $\beta =\ln 4$ ($k_{B}T=1/\ln 4=0.7213$). Also IGW at ${\beta }^{\prime }=0$ ($T^{\prime }=\infty$) corresponds to ISAW at $\beta =\ln 2$ ($k_{B}T=1/ln2=1.4427$). 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.

3 pages, 1 figure, REVTEX file

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