Monte Carlo Calculations. V. Three‐Dimensional Study of a General Bimolecular Interaction Potential

1964 ◽  
Vol 41 (8) ◽  
pp. 2377-2386 ◽  
Author(s):  
Don L. Bunker ◽  
Normand C. Blais
Keyword(s):  
Monte Carlo ◽  
Interaction Potential ◽  
Three Dimensional ◽  
Monte Carlo Calculations ◽  
Bimolecular Interaction

scholarly journals MONTE-CARLO CALCULATIONS OF PHASE TRANSITION TEMPERATURE IN THE ISING MODEL WITH LONG RANGE INTERACTIONS

2017 ◽  
Vol 21 (6) ◽  
pp. 161-170
Author(s):  
A.A. Biryukov ◽  
Y.V. Degtyarova
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Transition Temperature ◽  
Long Range ◽  
Phase Transition Temperature ◽  
Three Dimensional ◽  
Ising Models ◽  
Monte Carlo Calculations ◽  
Spin Interactions ◽  
Long Range Interactions

The article deals with two-dimensional and three-dimensional Ising models with the long-range spin interactions. The intensity of interaction between the spins relies decreasing with distance r as a power law r-d-σ with dimensional d and parameter σ. The research are conducted by Monte-Carlo method with Metropolis algorithm using parallel computing techniques. On the basis of nu- merical simulation the dependence of the phase transition temperature on the parameter σ is found. It is shown that at phase transition temperature decreases with increasing σ.

INTERFACE TENSIONS OF BINARY SYSTEMS

1992 ◽  
Vol 03 (05) ◽  
pp. 879-887 ◽  
Author(s):  
GERNOT MÜNSTER
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Low Temperatures ◽  
Binary Systems ◽  
Three Dimensional ◽  
Liquid Mixtures ◽  
Interface Tension ◽  
Monte Carlo Calculations ◽  
Pure Phases ◽  
Semiclassical Expansion

In liquid mixtures or analogous binary systems at low temperatures the pure phases may coexist, separated by an interface. The interface tension vanishes according to σ=σ0(1−T/Tc)µ as the temperature T approaches the critical point from below. Similarly the correlation length diverges as ξ=ξ0(T/Tc−1)−ν. For three-dimensional systems the dimensionless product R=σ0(ξ0)2 is universal. This and related universal quantities are investigated by means of a semiclassical expansion in the framework of Φ4 theory, as well as by Monte Carlo calculations in the three-dimensional Ising model.

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