Monte Carlo Studies of Random Impurity Effects in an Antiferromagnetic Ising Model on the Triangular Lattice

1986 ◽  
Vol 55 (2) ◽  
pp. 622-633 ◽  
Author(s):  
Fumitaka Matsubara
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Triangular Lattice ◽  
Impurity Effects ◽  
Monte Carlo Studies ◽  
Antiferromagnetic Ising Model

Monte Carlo studies of magnetism and superconductivity on the triangular lattice

2008 ◽  
Vol 103 (7) ◽  
pp. 07C717 ◽  
Author(s):  
Shi-Quan Su ◽  
Zhong-Bing Huang ◽  
Hai-Qing Lin
Keyword(s):  
Monte Carlo ◽  
Triangular Lattice ◽  
Monte Carlo Studies

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.

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