Improved Phenomenological Renormalization Schemes
Abstract
An analysis is made of various methods of phenomenological renormalization based on finitesize scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made using twodimensional Ising and Potts lattices and the threedimensional 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 finitesize scaling amplitude of the internal energy in the threedimensional Ising model. It is shown that the twodimensional Ising and Potts models contain no finitesize corrections to the internal energy so that the positions of the critical points for these models can be determined exactly from solutions for strips of finite width. It is also found that for the twodimensional Ising model the scaling finitesize equation for the derivative of the inverse correlation length with respect to temperature gives the exact value of the thermal critical exponent.
 Publication:

Soviet Journal of Experimental and Theoretical Physics
 Pub Date:
 August 2000
 DOI:
 10.1134/1.1311992
 arXiv:
 arXiv:condmat/0108002
 Bibcode:
 2000JETP...91..332Y
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 14 pages with 1 figure in latex