scholarly journals New Method of Monte Carlo Simulations and Phenomenological Theory of Phase Transition in the Two-Dimensional XY-Model

1977 ◽  
Vol 58 (2) ◽  
pp. 701-702 ◽  
Author(s):  
M. Suzuki ◽  
S. Miyashita ◽  
A. Kuroda
2008 ◽  
Vol 15 (05) ◽  
pp. 605-612 ◽  
Author(s):  
VLADIMIR P. ZHDANOV

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.


1989 ◽  
Vol 22 (14) ◽  
pp. L705-L709 ◽  
Author(s):  
S Sakamoto ◽  
F Yonezawa ◽  
K Aoki ◽  
S Nose ◽  
M Hori

2017 ◽  
Vol 28 (08) ◽  
pp. 1750099
Author(s):  
F. W. S. Lima

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios [Formula: see text], [Formula: see text], and [Formula: see text]. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.


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