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J. Phys. A: Math. Gen. 14 (1981) L91-L96. Printed in Grept Britain LETTER TO THE EDITOR
 

Summary: J. Phys. A: Math. Gen. 14 (1981) L91-L96. Printed in Grept Britain
LETTER TO THE EDITOR
q-state Potts models in d dimensions: Migdal-Kadanoff
approximation
D Andelman and A N Berker
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts
02139, USA
Received 27 October 1980
Abstract. The first- and second-order phase transitions of the q-state Potts models are
obtained in arbitrary dimension d. Critical and tricritical behaviours merge and annihilate
at q,(d), clearing the way to first-order transitions at q: q,(d) by the condensation of
effective vacancies. The value of q,(d) decreases with increasing d, from diverging as
exp[2/(d - l)] at d + 1+,to q,(2) = 3.81 (cf exact value of 4), to lower values at d : 2. For
given d, a changeover in critical behaviour occurs at ql(d),as the critical fixed points merge
from the Potts-lattice-gas region to the undiluted Potts limit. It is suggested that the power
law singularities of the percolation problem (q+ 1') have logarithmic corrections.
Potts (1952) models are composed of an array of local degrees of freedom, each of
which can be in one of q states. The energy is determinedonly by whether neighbouring
degrees of freedom are in the same state or not. As such, the q-state Potts models are a
generalisation of the Ising model (q= 2). These models achieved recognition because

  

Source: Andelman, David - School of Physics and Astronomy, Tel Aviv University

 

Collections: Materials Science; Physics