Cluster-variation method applied in the pair approximation to theS=1Ising ferromagnet having additional single-ion-type uniaxial anisotropy

1978 ◽  
Vol 17 (9) ◽  
pp. 3675-3683 ◽  
Author(s):  
Wai Man Ng ◽  
Jeremiah H. Barry
Keyword(s):  
Uniaxial Anisotropy ◽  
Cluster Variation Method ◽  
Pair Approximation ◽  
Variation Method ◽  
Cluster Variation

CLUSTER VARIATION APPROACH TO THE ANTIFERROMAGNETIC TRANSITION OF THE t-J MODEL

1993 ◽  
Vol 07 (27) ◽  
pp. 1761-1771 ◽  
Author(s):  
ANDREA DANANI ◽  
ALESSANDRO PELIZZOLA
Keyword(s):  
Phase Transition ◽  
Cluster Variation Method ◽  
Pair Approximation ◽  
Variation Method ◽  
Antiferromagnetic Phase ◽  
Antiferromagnetic Transition ◽  
Néel Temperature ◽  
Variation Approach ◽  
Symmetry Properties ◽  
Cluster Variation

The antiferromagnetic phase transition associated with the breaking of the magnetic SU(2) symmetry of the t-J model is investigated by means of the cluster variation method in the pair approximation. The disordered and antiferromagnetic phases are characterized by means of their symmetry properties, and an analytical implicit expression is given for the Néel temperature.

Continuous Displacement of “Lattice” Atoms

1992 ◽  
Vol 278 ◽  
Author(s):  
Ryoichi Kikuchi ◽  
Arezki Beldjenna
Keyword(s):  
Interatomic Potential ◽  
Rotational Symmetry ◽  
Cluster Variation Method ◽  
Lattice Points ◽  
Pair Approximation ◽  
Variation Method ◽  
Pair Probability ◽  
Integral Equation Formulation ◽  
Cluster Variation ◽  
Continuous Displacement

AbstractIn the existing CVM (Cluster Variation Method) formulations, atoms are placed on lattice points. A modification is proposed in which an atom can be displaced from a lattice point. The displaced position is written by a vector r, which varies continuously. This model is treated in the CVM framework by regarding an atom at r as a species r. The probability of finding an atom displaced at r in dr is written as f(r)dr, and the corresponding pair probability is written as g(r1, r2)dr1dr2. We formulate using the pair approximation of the CVM in the present paper. The interatomic potential is assumed given, for example as the Lennard-Jones form. The entropy is written in terms of f(r) and g(r1, r2) using the CVM formula. The special feature of the present formulation which is different from the prevailing no-displacement cases of the CVM is that rotational symmetry of the lattice is to be satisfied by the f(r) and g(r1, r2) functions. After the general equations are written in the continuum vector form and in the integral equation formulation, an example of a single-component system is solved by changing integrals into summations over finite intervals. Further we construct simulations of displacement patters in such a way that the pattern satisfies the pair probability distribution which has been calculated as the output of the CVM analysis. The simulated pattern shows the wavy behavior of phonons. Future directions are discussed.

General Algorithm for the Cluster-Variation Method

1983 ◽  
Vol 28 (5) ◽  
pp. 565-568 ◽  
Author(s):  
J S Desjardins ◽  
O Steinsvoll
Keyword(s):  
Cluster Variation Method ◽  
General Algorithm ◽  
Variation Method ◽  
Cluster Variation
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