Universality and tricritical behavior of three-dimensional Ising models with two- and four-spin interactions

1981 ◽  
Vol 24 (1) ◽  
pp. 347-354 ◽  
Author(s):  
O. G. Mouritsen ◽  
S. J. Knak Jensen ◽  
B. Frank
Keyword(s):  
Three Dimensional ◽  
Ising Models ◽  
Spin Interactions ◽  
Tricritical Behavior

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.

Nucleation and metastability in three-dimensional Ising models

1984 ◽  
Vol 36 (3-4) ◽  
pp. 447-470 ◽  
Author(s):  
Dieter W. Heermann ◽  
Antonio Coniglio ◽  
W. Klein ◽  
Dietrich Stauffer
Keyword(s):  
Three Dimensional ◽  
Ising Models

scholarly journals LOOPS, SURFACES AND GRASSMANN REPRESENTATION IN TWO- AND THREE-DIMENSIONAL ISING MODELS

1999 ◽  
Vol 14 (29) ◽  
pp. 4549-4574 ◽  
Author(s):  
C. R. GATTRINGER ◽  
S. JAIMUNGAL ◽  
G. W. SEMENOFF
Keyword(s):  
Three Dimensional ◽  
Ising Models ◽  
Algebraic Representation ◽  
Simple Derivation ◽  
Counting Problems ◽  
Intrinsic Geometry ◽  
Geometry Factor ◽  
Loop Expansion ◽  
Loop Surface

We construct an algebraic representation of the geometrical objects (loop and surface variables) dual to the spins in 2 and 3D Ising models. This algebraic calculus is simpler than dealing with the geometrical objects, in particular when analyzing geometry factors and counting problems. For the 2D case we give the corrected loop expansion of the free energy and the radius of convergence for this series. For the 3D case we give a simple derivation of the geometry factor which prevents overcounting of surfaces in the intrinsic geometry representation of the partition function, and find a classification of the surfaces to be summed over. For 2 and 3D we derive a compact formula for 2n-point functions in loop (surface) representation.

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