Minimalistic real-space renormalization of Ising and Potts Models in two dimensions

We introduce and discuss a real-space renormalization group (RSRG) procedure on very small lattices, which in principle does not require any of the usual approximations, e.g., a cut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carried out numerically on very small lattices (4×4 to 2×2) and implemented for the Ising Model and the q = 3,4,5-state Potts Models. Nevertheless, the resulting estimates of the correlation length exponent and the magnetization exponent are typically within 3–7% of the exact values. The 4-state Potts Model generates a third magnetic exponent, which seems to be unknown in the literature. A number of questions about the meaning of certain exponents and the procedure itself arise from its use of symmetry principles and its application to the q 5 Potts Model. =