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J. Phys. A: Math. Gen. 13 (1980)L413-L418. Printed in Great Britain LETTER TO THE EDITOR
 

Summary: J. Phys. A: Math. Gen. 13 (1980)L413-L418. Printed in Great Britain
LETTER TO THE EDITOR
First- and second-order phase transitions of infinifemstate
Potts models in one dimension
A N Berker, D Andelman and A Aharony?
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts
02139. USA
Received 27 August 1980
Abstract. The q-state, ddimensional Potts models exhibit a variety of phase-transition
behaviour in the limit d + li, q +03, and I (d -1)In q finite. The regions I <1, 1 and 2 new changeover phenomenon at I =In 4),and first-order transitions. The latter are due lo
the condensation of effective vacancies. Critical and tricritical exponent values are given.
Experimental realisations (Alexander 1975, Aharony et a1 1977)and connections with
percolation (Fortuinand Kasteleyn 1969)are reasons for the current high interest in the
phase transitions of the q-state Potts (1952) models. Another reason is a sustained
conceptual development for spatial dimension d = 2, from rigorous (Baxter 1973,
1979), conjectural (den Nijs 1979, Nienhuis et a1 1979, 1980b, Nauenberg and
Scalapino 1980) and approximate (Nienhuis et a1 1979, 1980a,b) theories. These
theories show that the phase transitions of the Potts models change from second to first

  

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

 

Collections: Materials Science; Physics