Two-dimensional-lattice spin models with long-range antiferromagnetic interactions

1991 ◽  
Vol 44 (13) ◽  
pp. 7066-7069 ◽  
Author(s):  
S. Romano
Keyword(s):  
Long Range ◽  
Two Dimensional ◽  
Spin Models ◽  
Dimensional Lattice ◽  
Lattice Spin ◽  
Lattice Spin Models

INFLUENCE OF THE INITIAL SOURCE OF EPIDEMIC AND PREVENTIVE VACCINATION ON THE SPREADING PHENOMENA IN A TWO-DIMENSIONAL LATTICE

2004 ◽  
Vol 15 (06) ◽  
pp. 755-765 ◽  
Author(s):  
R. A. KOSIŃSKI ◽  
Ł. ADAMOWSKI
Keyword(s):  
Long Range ◽  
Probabilistic Model ◽  
Small World ◽  
Two Dimensional ◽  
Small World Networks ◽  
Spreading Process ◽  
Dimensional Lattice ◽  
Epidemic Curve ◽  
Preventive Vaccination ◽  
Initial Source

The probabilistic model of epidemic in a two-dimensional lattice with an additional random, long range connections characteristic for the small world networks is presented. Relations describing the spreading process of epidemics, like epidemic curve or range of epidemic in time, were found. The influence of the borders of the lattice and the localization of the initial source of epidemic on the epidemic curve is found analytically. The application of the preventive vaccination in the population is discussed.

NUMERICAL STUDY OF THE 3-COLOR PROBLEM ON CUBIC LATTICE BY A METHOD OF RANDOM PARTITION FUNCTIONS

1994 ◽  
Vol 08 (07) ◽  
pp. 439-443
Author(s):  
A. V. BAKAEV ◽  
V. I. KABANOVICH
Keyword(s):  
Numerical Study ◽  
Stochastic Method ◽  
Partition Functions ◽  
Random Partition ◽  
Spin Models ◽  
Cubic Lattice ◽  
Color Problem ◽  
Lattice Spin ◽  
Finite Lattices ◽  
Lattice Spin Models

We propose a stochastic method for computing partition functions of models which can be stated as lattice spin models. The method admits averaging over independent realizations, thus is well suited for simulating models on finite lattices. We apply this method to the 3-color problem on cubic map.

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