scholarly journals Variational and Mean Field Formulations of the Cluster Variation Method and of the Path Probability Method

1994 ◽  
Vol 115 ◽  
pp. 255-272 ◽  
Author(s):  
François Ducastelle
Keyword(s):  
Mean Field ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Probability Method ◽  
Cluster Variation ◽  
Path Probability Method

Multi-Scale Phase Field Simulation of Disorder-Order Transition, Combined with Cluster Variation and Path Probability Methods

2009 ◽  
Vol 631-632 ◽  
pp. 401-406
Author(s):  
Munekazu Ohno ◽  
Ying Chen ◽  
Tetsuo Mohri
Keyword(s):  
Phase Field ◽  
Cluster Variation Method ◽  
Field Method ◽  
Phase Field Method ◽  
Variation Method ◽  
Probability Method ◽  
Multi Scale ◽  
Probability Methods ◽  
Cluster Variation ◽  
Path Probability Method

Multi-scale simulation of ordering process from electronic, atomistic scales to microstructural scale was carried out by hybridizing Phase Field Method (PFM) and Cluster Variation Method (CVM). The hybrid model was applied to disorder-L10 ordering process in Fe-Pd system. Furthermore, computation of relaxation constants in the PFM was attempted based on Path Probability Method (PPM) which is the time evolution version of the CVM, within a linearized analysis of order-order relaxation process.

CRITICAL TEMPERATURES AND MEAN-FIELD CRITICAL COEFFICIENTS FOR THE HEISENBERG MODEL BASED ON CVM

1992 ◽  
Vol 06 (13) ◽  
pp. 2363-2374
Author(s):  
GIICHI TANAKA ◽  
MINORU KIMURA
Keyword(s):  
Heisenberg Model ◽  
Mean Field ◽  
Three Dimensional ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Critical Temperatures ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Cluster Variation

Critical temperatures T c and mean-field critical coefficients [Formula: see text] for susceptibilities are calculated by a cluster-variation method (CVM) for a three-dimensional Heisenberg model on a simple cubic lattice. Both the full CVM based on a 4-spin cluster and the SCVM are applied and the same values for T c and [Formula: see text] are obtained by three different approximation in the SCVM. The results are compared with those obtained by the same approach for the three-dimensional Ising model on the simple cubic lattice.

Theoretical Study of Glass Transition Based on Cluster Variation Method

2007 ◽  
Vol 539-543 ◽  
pp. 2425-2430 ◽  
Author(s):  
Tetsuo Mohri ◽  
Yoshitaka Kobayashi
Keyword(s):  
Free Energy ◽  
Glass Transition ◽  
Order Parameter ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Bravais Lattice ◽  
Probability Method ◽  
Temperature Dependent Viscosity ◽  
Viscosity Term ◽  
Cluster Variation

Modeling of Glass transition is attempted based on the Cluster Variation Method. Free energy functional of an L10 ordered phase is employed to describe the first order nature of the transition. Free energy contour surface calculated as a function of temperature and an order parameter which simulates an amount of defects provides a generalized stability diagram in which the ideal glass transition temperature is identified as a critical point. Transition kinetics is investigated by Path Probability Method which is the kinetics version of the CVM to time domain. Continuous cooling behavior is calculated by explicitly incorporating the temperature dependent viscosity term based on VFT (Vogel-Fulcher-Tamman) formula. The glass transition is realized as the freezing of the order parameter due to the enhanced viscosity. The extension of the present theoretical scheme to non-Bravais lattice is attempted by Continuous Cluster Variation Method.

Critical Behaviour of the Ferromagnetic Spin-3/2 – Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

2007 ◽  
Vol 62 (3-4) ◽  
pp. 127-139 ◽  
Author(s):  
M. Ali Pınar ◽  
Mustafa Keskin ◽  
Ahmet Erdinç ◽  
Osman Canko
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Phase Diagrams ◽  
Mean Field ◽  
Cluster Variation Method ◽  
Field Approximation ◽  
Critical Behaviour ◽  
Mean Field Approximation ◽  
Variation Method ◽  
Cluster Variation

The critical behaviour of the ferromagnetic spin-3/2 Blume-Emery-Griffiths model with repulsive biquadratic coupling in the absence and presence of an external magnetic field is studied by using the lowest approximation of the cluster variation method, which is identical with the mean-field approximation. Thermal variations of the order parameters are investigated for different values of the interaction parameters and the external magnetic field. The complete phase diagrams of the system are calculated in the (kT/J,K/J), (kT/J,D/J) and (kT /J,H/J) planes. Five new phase diagram topologies are obtained, which are either absent from previous approaches or have gone unnoticed. A detailed discussion and comparison of the phase diagrams is made.

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