scholarly journals Monte Carlo study of an extended three-state Potts model on the triangular lattice

2003 ◽  
Vol 67 (5) ◽  
Author(s):  
Z. F. Wang ◽  
B. W. Southern ◽  
D. A. Lavis
Keyword(s):  
Monte Carlo ◽  
Potts Model ◽  
Triangular Lattice ◽  
Monte Carlo Study

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.

scholarly journals Monte-Carlo Study of the Collective Behavior in Animal Group: A \(q\)-state Potts model

2015 ◽  
Vol 25 (3) ◽  
pp. 203
Author(s):  
Nguyen Phuoc The ◽  
Ngo Van Thanh
Keyword(s):  
Monte Carlo ◽  
Potts Model ◽  
Internal State ◽  
Monte Carlo Study ◽  
External Perturbation ◽  
Animal Group ◽  
Monte Carlo Simulation Technique ◽  
First Order ◽  
Group A ◽  
Transition Behaviour

We study in this work the phase transition behaviour of animal groups. We assume that the individuals in the group have two classes of state. One is the internal state which can be either excited or non-excited. The other one is characterized by their orientation or direction of motion, it is so called the external state.The internal state plays an important role in the rules of interaction between the individuals.The system is put under a source of external perturbation called ``noise", the individuals can freely move from one site to another site on a two-dimension triangular lattice. We use the Monte-Carlo simulation technique for studying the behavior of the model with varying noise. For simplicity, we consider the orientation of individuals which has $q$ states as in the Potts model. We show that the system has three phases which correspond to the uncollected, flocking and runaway behaviors at very low, medium and high noise, respectively. These phases are separated by two first-order transitions.

ORDERING PROBLEM FOR THE ANTIFERROMAGNETIC POTTS MODEL: T=0 MONTE-CARLO STUDIES

1991 ◽  
Vol 05 (19) ◽  
pp. 3061-3071 ◽  
Author(s):  
A.V. BAKAEV ◽  
V.I. KABANOVICH ◽  
A.M. KURBATOV
Keyword(s):  
Monte Carlo ◽  
Long Range ◽  
Potts Model ◽  
Triangular Lattice ◽  
Lattice Models ◽  
Range Order ◽  
Square Lattice ◽  
Long Range Order ◽  
Monte Carlo Studies ◽  
Antiferromagnetic Potts Model

AF Potts model MC dynamics at T=0 is considered. It is shown that q=3 square lattice and q=4 triangular lattice models are frozen for local MC algorithm. The nature of the previously discussed long-range order phases is examined and entropically favored states are considered.

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