Exact cluster size distribution in the one-dimensional Ising model

2005 ◽  
Vol 71 (2) ◽  
Author(s):  
M. B. Yilmaz ◽  
Frank M. Zimmermann
Keyword(s):  
Ising Model ◽  
Size Distribution ◽  
Cluster Size ◽  
Cluster Size Distribution ◽  
One Dimensional ◽  
The One

scholarly journals On bimodal size distribution of spin clusters in the onedimensional Ising model

2018 ◽  
Vol 182 ◽  
pp. 03004
Author(s):  
A. Ivanytskyi ◽  
V. Chelnokov
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Size Distribution ◽  
Lattice Constant ◽  
Finite Size ◽  
Bimodal Size Distribution ◽  
One Dimensional ◽  
Spin Clusters ◽  
The One ◽  
Finite Extent

The size distribution of geometrical spin clusters is exactly found for the onedimensional Ising model of finite extent. For the values of lattice constant β above some “critical value” βc the found size distribution demonstrates the non-monotonic behaviour with the peak corresponding to the size of the largest available cluster. In other words, for high values of the lattice constant there are two ways to fill the lattice: either to form a single largest cluster or to create many clusters of small sizes. This feature closely resembles the well-know bimodal size distribution of clusters which is usually interpreted as a robust signal of the first order liquid-gas phase transition in finite systems. It is remarkable that the bimodal size distribution of spin clusters appears in the one-dimensional Ising model of finite size, i.e. in the model which in thermodynamic limit has no phase transition at all.

Evolution of cluster size distribution in nucleation and growth processes

1991 ◽  
Vol 136 (3) ◽  
pp. 181-197 ◽  
Author(s):  
J. Bartels ◽  
U. Lembke ◽  
R. Pascova ◽  
J. Schmelzer ◽  
I. Gutzow
Keyword(s):  
Size Distribution ◽  
Cluster Size ◽  
Nucleation And Growth ◽  
Cluster Size Distribution ◽  
Growth Processes

Bimodality of cluster-size distribution and condensation in a finite Lennard-Jones system

1981 ◽  
Vol 24 (6) ◽  
pp. 2893-2902 ◽  
Author(s):  
Julian H. Gibbs ◽  
Biman Bagchi ◽  
Udayan Mohanty
Keyword(s):  
Size Distribution ◽  
Cluster Size ◽  
Cluster Size Distribution ◽  
Lennard Jones
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