scholarly journals Coherent-Anomaly Analysis with Cluster Variation Method for Two-Dimensional Ising Model with Nearest-Neighbor and Next-Nearest-Neighbor Interactions

1994 ◽  
Vol 115 ◽  
pp. 221-235 ◽  
Author(s):  
Kazuyuki Tanaka ◽  
Tsuyoshi Horiguchi ◽  
Tohru Morita
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Two Dimensional ◽  
Anomaly Analysis ◽  
Cluster Variation

scholarly journals Chain length probability distribution — equivalence of ASYNNNI and 1d Ising model

Open Physics ◽  
2008 ◽  
Vol 6 (2) ◽  
Author(s):  
Mirjana Milić
Keyword(s):  
Ising Model ◽  
Probability Distribution ◽  
Chain Length ◽  
Nearest Neighbor ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Ising Chain ◽  
High Tc ◽  
One Dimensional ◽  
Cluster Variation

AbstractAn expression for the chain length probability distribution p(l) of a one dimensional Ising chain was derived using the cluster variation method formalism, the p(l) being expressed through the pair cluster probabilities. It was shown numerically that the same expression also applies in the case of one dimensional chains formed along one of the next-nearest neighbor interactions included in the two dimensional ASYNNNI (Asymmetric Next-Nearest Neighbor Ising) model, widely used to describe the statistics of oxygen ordering in the basal CuOx planes of the YBa2Cu3O6+x type high-Tc superconducting materials. Equivalency between ASYNNNI and 1d Ising model is discussed.

scholarly journals The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 319
Author(s):  
Alianna J. Maren
Keyword(s):  
Free Energy ◽  
Nearest Neighbor ◽  
Activation Enthalpy ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Energy Minimum ◽  
Dimensional Parameter ◽  
Free Energy Minimum ◽  
Interaction Enthalpy ◽  
Cluster Variation

One of the biggest challenges in characterizing 2-D image topographies is finding a low-dimensional parameter set that can succinctly describe, not so much image patterns themselves, but the nature of these patterns. The 2-D cluster variation method (CVM), introduced by Kikuchi in 1951, can characterize very local image pattern distributions using configuration variables, identifying nearest-neighbor, next-nearest-neighbor, and triplet configurations. Using the 2-D CVM, we can characterize 2-D topographies using just two parameters; the activation enthalpy (ε0) and the interaction enthalpy (ε1). Two different initial topographies (“scale-free-like” and “extreme rich club-like”) were each computationally brought to a CVM free energy minimum, for the case where the activation enthalpy was zero and different values were used for the interaction enthalpy. The results are: (1) the computational configuration variable results differ significantly from the analytically-predicted values well before ε1 approaches the known divergence as ε1→0.881, (2) the range of potentially useful parameter values, favoring clustering of like-with-like units, is limited to the region where ε0<3 and ε1<0.25, and (3) the topographies in the systems that are brought to a free energy minimum show interesting visual features, such as extended “spider legs” connecting previously unconnected “islands,” and as well as evolution of “peninsulas” in what were previously solid masses.

Phase Transformations in Hexagonal-Close-Packed Alloys: Analysis with the Cluster Variation Method

1992 ◽  
Vol 291 ◽  
Author(s):  
Ryan Mccormack ◽  
Mark Asta ◽  
Gerbrand Ceder ◽  
Didier de Fontaine
Keyword(s):  
Nearest Neighbor ◽  
Binary Alloys ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Temperature Phase ◽  
Hexagonal Close Packed ◽  
Cluster Configuration ◽  
Cluster Variation ◽  
Polyhedron Method ◽  
Pair Interactions

ABSTRACTWe present a study of the hexagonal close-packed (hcp) Ising model for binary alloys within the cluster variation approximation. Groundstates of order stabilized by nearest-neighbor (NN) pair, triplet, and tetrahedron interactions were determined using the cluster configuration polyhedron method; no previous hcp ground-state study has considered all of these interactions. We predict physically realizable groundstates with stoichiometries A, AB (3 distinct structures), A2B, A3B, and A4B3. The previously unpredicted A4B3 structure is stabilized by multiatom (i.e. triplet, tetrahedron) interactions, while the others are stabilized by the two NN pair interactions. The Cluster Variation Method (CVM) was used to calculate the finite-temperature phase-equilibria for prototypical binary alloys. We present the first ordering phase diagrams computed with the CVM which contain all relevant groundstates for both isotropic and anisotropic NN pair interactions.

Cluster variation method for two-dimensional Hubbard and t-J models

1994 ◽  
Vol 235-240 ◽  
pp. 2187-2188 ◽  
Author(s):  
Kazunuki Tanaka ◽  
Hiromichi Ebisawa ◽  
Tohru Morita
Keyword(s):  
Cluster Variation Method ◽  
Variation Method ◽  
Two Dimensional ◽  
Cluster Variation

Order—Disorder Behavior of Grain Boundaries in a two Dimensional Mcdel Ordered Alloy

1986 ◽  
Vol 81 ◽  
Author(s):  
Diana Farkas ◽  
Ho Jang
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Pair Interaction ◽  
Cluster Variation Method ◽  
Boundary Region ◽  
Variation Method ◽  
Two Dimensional ◽  
Interaction Energies ◽  
Disordered Layer ◽  
Cluster Variation

AbstractThe order-disorder behavior of a Σ = 5 grain boundary was investigated using a two dimensional latice gas model and the cluster variation method. It is found that a disordered layer forms in the grain boundary region at temperatures significantly below theorder—disorder temperature for the bulk. Under certain assumptions for the pair interaction energies the model predicts grain boundary compositions different from the bulk.

Sign in / Sign up

Export Citation Format

Share Document