Improved Phenomenological Renormalization Schemes

M. A. Yurishchev

Radiophysical Research Institute, Nizhni Novgorod, 606263 Russia*
e-mail: yur@nirfi.sci-nnov.ru

Received March 22, 2000

Abstract—An analysis is made of various methods of phenomenological renormalization based on finite-
dimensional scaling equations for inverse correlation lengths, the singular part of the free energy density, and
their derivatives. The analysis is made using two-dimensional Ising and Potts lattices and the three-dimensional
Ising model. Variants of equations for the phenomenological renormalization group are obtained which ensure
more rapid convergence than the conventionally used Nightingale phenomenological renormalization scheme.
An estimate is obtained for the critical finite-dimensional scaling amplitude of the internal energy in the three-
dimensional Ising model. It is shown that the two-dimensional Ising and Potts models contain no finite-dimen-
sional corrections to the internal energy so that the positions of the critical points for these models can be deter-
mined exactly from solutions for strips of finite width. It is also found that for the two-dimensional Ising model
the scaling finite-dimensional equation for the derivative of the inverse correlation length with respect to tem-
perature gives the exact value of the thermal critical index. © 2000 MAIK “Nauka/Interperiodica”.

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