Migdal-Kadanoff renormalization for the exchange interaction model

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Thomas A. Larsson

Robert H. Swendsen, Royce K. P. Zia

H. H. Chen, Felix Lee

Through use of an approximation introduced by Suzuki and Takano, the Migdal-Kadanoff (MK) renormalization-group transformation with the rescaling length b=2 is derived for the exchange-interaction (EI) model. Both the standard MK method and its modification, which preserves the free energy in the renormalization transformation, are used to determine critical temperatures and thermal exponents of the EI model on cubic lattices for various spins.

H. H. Chen, Felix Lee, H. C. Tseng

A modification of the Migdal-Kadanoff (MK) real-space renormalization technique is studied and applied to the q-state Potts model on the square and the simple cubic lattices. A parameter x which describes the boundary condition is introduced to the cluster-decimation (CD) approximation. When x=2, the present method is the same as the CD approximation, and in the limit x\ensuremath{\rightarrow}\ensuremath{\infty} this method reduces to the MK technique. Critical temperatures and exponents of the Potts model are calculated for 0<q\ensuremath{\le}4 by using various boundary conditions. Very good estimates of critical properties are obtained. The choice of the boundary condition is discussed.

Ying‐Chieh Chen, H. H. Chen, Felix Lee