Polygons on the honeycomb lattice

Abstract

The authors enumerated the number of self-avoiding polygons on the honeycomb lattice to 82 steps. Analysis of the resulting series gives for the connective constant mu =1.8477594+or-6*10-6, in agreement with Nienhuis' value (1984) of mu =(2+2)12/=1.84775906. . .. The critical exponent alpha =0.4999+or-10-4 (unbiased), or alpha =0.49998+or-2*10$0-5 (biased). A non-physical singularity on the negative real axis is accurately located, and some curious results concerning the confluent singularity are obtained.