Monte Carlo study of the Potts model on the square and the simple cubic lattices

1989 ◽  
Vol 40 (7) ◽  
pp. 5007-5014 ◽  
Author(s):  
Chin-Kun Hu ◽  
Kit-Sing Mak
Keyword(s):  
Monte Carlo ◽  
Potts Model ◽  
Monte Carlo Study ◽  
Cubic Lattices ◽  
Simple Cubic

scholarly journals 3D ISING NONUNIVERSALITY: A MONTE CARLO STUDY

2005 ◽  
Vol 16 (08) ◽  
pp. 1217-1224 ◽  
Author(s):  
MELANIE SCHULTE ◽  
CAROLINE DROPE
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
External Field ◽  
Nearest Neighbor ◽  
Monte Carlo Study ◽  
Universality Class ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Binder Cumulant

We investigate as a member of the Ising universality class the Next-Nearest Neighbor Ising model without external field on a simple cubic lattice by using the Monte Carlo Metropolis Algorithm. The Binder cumulant and the susceptibility ratio, which should be universal quantities at the critical point, were shown to vary for small negative next-nearest neighbor interactions.

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.

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