Monte Carlo renormalization-group study of thed=3planar model

The $d=3\mathrm{}$ planar model is analyzed for the first time with the Monte Carlo renormalization-group (MCRG) method. To increase the efficiency of the calculation, an operator is introduced in analogy with the "vacancy" operator used in the MCRG analysis of the $q=4\mathrm{}$ Potts model. This operator is shown to be important in understanding the effect of the renormalization transformation on the Hamiltonian, and in improving the convergence of the method.