Renormalization-group study of the Hamiltonian version of the Potts model. II. Self-dual renormalization-group treatment

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Abstract
The one-dimensional Hamiltonian version of the two-dimensional Potts model is studied by the application of a self-dual renormalization-group transformation. Blocks containing up to 11 sites are considered and mapped onto new, equivalent Potts spins by keeping the lowest-lying levels only. The higher-lying states are also taken into account in a perturbational way for smaller cells. Unfortunately, this renormalization-group treatment cannot reproduce the first-order transition for large values of the number of states, and the critical exponents for the three- and four-state Potts model do not seem to converge to the conjectured results as larger and larger blocks are taken.