scholarly journals Monte Carlo renormalization-group study of domain growth in the Potts model on a triangular lattice

1990 ◽  
Vol 41 (7) ◽  
pp. 4663-4668 ◽  
Author(s):  
Christopher Roland ◽  
Martin Grant
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Potts Model ◽  
Triangular Lattice ◽  
Domain Growth ◽  
Monte Carlo Renormalization Group

A Monte Carlo and renormalization group study of the Ising model with nearest and next nearest neighbor interactions on the triangular lattice

1983 ◽  
Vol 61 (11) ◽  
pp. 1515-1527 ◽  
Author(s):  
James Glosli ◽  
Michael Plischke
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Ising Model ◽  
Potts Model ◽  
Triangular Lattice ◽  
Nearest Neighbor ◽  
Universality Class ◽  
Energy Functional ◽  
First Order ◽  
Universality Classes

The Ising model with nearest and next nearest neighbor antiferromagnetic interactions on the triangular lattice displays, for Jnnn/Jnn = 0.1, three phase transitions in different universality classes as the magnetic field is increased. We have studied this model using Monte Carlo and renormalization group techniques. The transition from the paramagnetic to the 2 × 1 phase (universality class of the Heisenberg model with cubic anisotropy) is found to be first order; the transition from the paramagnetic phase to the [Formula: see text] phase (universality class of the three state Potts model) is continuous; and the transition from the paramagnetic to the 2 × 2 phase (universality class of the four state Potts model) is found to change from first order to continuous as the field is increased. We have mapped out the phase diagram and determined the critical exponents for the continuous transitions. A novel technique, using a Landau-like free energy functional determined from Monte Carlo calculations, to distinguish between first order and continuous transitions, is described.

CRITICAL POINT OF THE KAGOME POTTS MODEL: A HISTOGRAM MONTE CARLO RENORMALIZATION GROUP DETERMINATION

1994 ◽  
Vol 08 (07) ◽  
pp. 455-459 ◽  
Author(s):  
CHIN-KUN HU ◽  
JAU-ANN CHEN ◽  
F. Y. WU
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Critical Point ◽  
Potts Model ◽  
Group Method ◽  
Renormalization Group Method ◽  
Kagome Lattice ◽  
Kagomé Lattice ◽  
Monte Carlo Renormalization Group

The histogram Monte Carlo renormalization group method proposed by Hu is used to determine the critical point of the q-state Potts model on the Kagome lattice. Our results are compared with the predictions of conjectures by Wu and Tsallis.

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