Order of phase transition for systems with multispin interactions: Monte Carlo simulations

1986 ◽  
Vol 34 (7) ◽  
pp. 4885-4888 ◽  
Author(s):  
Francisco C. Alcaraz
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Order Of Phase Transition ◽  
Multispin Interactions

AVRAMI–KOLMOGOROV–JOHNSON–MEHL KINETICS FOR NANOPARTICLES

2008 ◽  
Vol 15 (05) ◽  
pp. 605-612 ◽  
Author(s):  
VLADIMIR P. ZHDANOV
Keyword(s):  
Phase Transition ◽  
Activation Energy ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Infinite Medium ◽  
Local State ◽  
Elementary Reaction ◽  
Regular Surface

In the conventional Avrami–Kolmogorov–Johnson–Mehl model, the reaction or phase transition occurring in the 2D or 3D infinite medium is considered to start and proceed around randomly distributed and/or appearing nucleation centers. The radius of the regions transformed is assumed to linearly increase with time. The Monte Carlo simulations presented, illustrate what may happen if the transformation takes place in nanoparticles. The attention is focused on nucleation on the regular surface, edge and corner sites, and on the dependence of the activation energy for elementary reaction events on the local state of the sites.

Transition under noise in the Sznajd model on square lattice

2016 ◽  
Vol 27 (03) ◽  
pp. 1650026 ◽  
Author(s):  
F. W. S. Lima
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Social Behavior ◽  
Monte Carlo Simulations ◽  
Order Phase Transition ◽  
Opinion Dynamics ◽  
Two Dimensions ◽  
Square Lattice ◽  
Behavior Model ◽  
Second Order Phase Transition

In order to describe the formation of a consensus in human opinion dynamics, in this paper, we study the Sznajd model with probabilistic noise in two dimensions. The time evolution of this system is performed via Monte Carlo simulations. This social behavior model with noise presents a well defined second-order phase transition. For small enough noise q < 0.33 most agents end up sharing the same opinion.

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