Improved Transfer-Matrix Schemes of Phenomenological Renormalization

Abstract

Different phenomenological RG transformations based on scaling relations for the derivatives of the inverse correlation length and singular part of the free-energy density are considered. These transformations are tested on the 2D square Ising and Potts models as well as on the 3D simple-cubic Ising model. Variants of RG equations yielding more accurate results than Nightingale's RG scheme are obtained. In the 2D case the finite-size equations which give the {\it exact} values of the critical point or the critical exponent are found.

LATTICE99(spin), 3 pages, no figures; to be published in Nucl. Phys. B (Proc. Suppl.)

Cited by in corpus (3)

• Critical temperatures of the three- and four-state Potts models on the kagome lattice
• Universality in the partially anisotropic three-dimensional Ising lattice
• Double Potts chain and exact results for some two-dimensional models