Minimalistic real-space Renormalization of 4x4 Ising and Potts Models in two dimensions - Willis,G; Pruessner,G; Keelan,J (Frontiers in Physics, 2015)
We introduce and discuss a real-space renormalization group (RSRG) procedure on verysmall lattices, which in principle does not require any of the usual approximations, e.g., acut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carriedout numerically on very small lattices (4×4 to 2×2) and implemented for the Ising Modeland the q = 3, 4, 5-state Potts Models. Nevertheless, the resulting estimates of thecorrelation length exponent and the magnetization exponent are typically within 3–7% ofthe exact values. The 4-state Potts Model generates a third magnetic exponent, whichseems to be unknown in the literature. A number of questions about the meaning ofcertain exponents and the procedure itself arise from its use of symmetry principles andits application to the q = 5 Potts Model.