Percolation renormalization-group approach to the<i>q</i>-state Potts model

Abstract

Based on the connection between the q-state Potts model (QPM) and the q-state bond-correlated percolation model (QBCPM), we have proposed percolation renormalization-group (PRG) methods to calculate the free energy, the critical point, and critical exponents for the QPM. Our methods are free from inconsistency in Larsson's method. We have carried out the ${\ensuremath{\lambda}}_{1}$\ifmmode\times\else\texttimes\fi{}${\ensuremath{\lambda}}_{1}$ to ${\ensuremath{\lambda}}_{2}$\ifmmode\times\else\texttimes\fi{}${\ensuremath{\lambda}}_{2}$ renormalization-group (RG) transformations in our methods for several values of original cell sizes ${\ensuremath{\lambda}}_{1}$ and final cell sizes ${\ensuremath{\lambda}}_{2}$ with various boundary conditions. We find that such RG transformations with large ${\ensuremath{\lambda}}_{1}$ and ${\ensuremath{\lambda}}_{2}$ and periodic boundary condition usually give accurate physical quantities for the QPM. The advantages and generalization of our approach are also discussed.