TY - JOUR
T1 - Q-state Potts models in d dimensions
T2 - Migdal-Kadanoff approximation
AU - Andelman, D.
AU - Berker, A. N.
PY - 1981
Y1 - 1981
N2 - 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 qc(d), clearing the way to first-order transitions at q>qc(d) by the condensation of effective vacancies. The value of qc(d) decreases with increasing d, from diverging as exp(2/(d-1)) at d to 1+, to qc(2)=3.81 (cf exact value of 4), to lower values at d>2. For given d, a changeover in critical behaviour occurs at q1(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 to 1+) have logarithmic corrections.
AB - 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 qc(d), clearing the way to first-order transitions at q>qc(d) by the condensation of effective vacancies. The value of qc(d) decreases with increasing d, from diverging as exp(2/(d-1)) at d to 1+, to qc(2)=3.81 (cf exact value of 4), to lower values at d>2. For given d, a changeover in critical behaviour occurs at q1(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 to 1+) have logarithmic corrections.
UR - https://www.scopus.com/pages/publications/4244026148
U2 - 10.1088/0305-4470/14/4/005
DO - 10.1088/0305-4470/14/4/005
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AN - SCOPUS:4244026148
SN - 0305-4470
VL - 14
SP - L91-L96
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 4
M1 - 005
ER -