CRITICAL-POINT OF THE KAGOME-POTTS MODEL - A MONTE-CARLO RENORMALIZATION-GROUP AND SCALING DETERMINATION

The determination of the critical point of the q-state Potts model on the Kagome lattices has been an outstanding unsolved problem Here we s tudy this problem by regarding the Potts model as generating correlate d bond percolations. By applying a combination of Monte Carlo renormal ization group and finite-size scaling analyses to the percolation prob lem, numerical estimates with an accuracy of 0.01% are obtained for th e Kagome critical point for q = 1,2, 3, 4. Our results for q = 1 are c onsistent with a recent highly accurate numerical estimate by Ziff and Suding, and results for q = 2 agree with:the known exact result withi n the numerical accuracy. Compared with results obtained in a recent s eries analysis by Jensen er al, our numbers differ from theirs slightl y for q = 3, and agree with theirs with a slightly better accuracy for q = 4. Our numbers also confirm that a conjecture due to Wu is extrem ely accurate.