Readings on Cluster Variation Theory – with Annotated Bibliography/Abstracts of Most Essential Sources

Essential Readings on Cluster Variation Method – Annotated Bibliography and/or Abstracts

• Pelizzola, Alessandro (2005), Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models, J. Phys. A: Math.Gen., 38, R309. Abstract: The cluster variation method (CVM) is a hierarchy of approximate variational techniques for discrete (Ising-like) models in equilibrium statistical mechanics, improving on the mean-field approximation and the Bethe–Peierls approximation, which can be regarded as the lowest level of the CVM. In recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models. The foundations of the CVM are briefly reviewed, and the relations with similar techniques are discussed. The main properties of the method are considered, with emphasis on its exactness for particular models and on its asymptotic properties. The problem of the minimization of the variational free energy, which arises in the CVM, is also addressed, and recent results about both provably convergent and message-passing algorithms are discussed. See further links to Pelizzola’s works.

Additional Readings on Cluster Variation Method – To-Read Stash

• Sanchez, J.M., Ducastelle, F., Gratias, D. (1984). Generalized cluster description of multicomponent systems. Physica 128A, 334-350. (available as download from Research Gate, use keywords)
• Schlijper, A.G., & Smit, B. (1992). A simple theory of weakly inhomogeneous fluids, Fluid Phase Equilibria, 76, 11-20. pdf
• Wang, C., & Zhou, H-J. (2013). Simplifying generalized belief propagation on redundant region graphs, Proc. Intl Meeting on Inference, Computation, and Spin Glasses, (July 28-30, 2013, Sapporo, Japan). arXiv
• Tepesch, Patrick D., Astra, Mark, & Ceder, Gerbrand. (1990). Computation of configurational entropy using Monte-Carlo probabilities in cluster-variation-method entropy expressions, Modelling Simul. Mater. Sci. Eng., 6 787, also Preprint (August 20, 1998).
• Tepesch, Patrick D., Astra, Mark, & Ceder, Gerbrand. (1990). Computation of configurational entropy using Monte-Carlo probabilities in cluster-variation-method entropy expressions, Modelling Simul. Mater. Sci. Eng., 6 787, also Preprint (August 20, 1998).

More on Cluster Variation Method – Slush Pile

• Sluiter, Marcel (Dec 09 2004), Illustration and intuitive derivation of the Cluster Variation Method originated by Ryoichi Kikuchi (1919-2003). Class project. Website listing Sluiter’s work but NOT including this class project, which seems no longer available. MATLAB or Maple Code to compute and plot the spinodal points as functions of T. Cumbersome expression of equations; up to three pages for a single equation – no substitutions of terms. I absolutely refuse to check this kind of work, but list it for completeness. His analysis is at equiatomic composition point, N(A) = N(B) = 0.5. Also, EnergyA) = Energy(B) = 0; the only energy term comes from interaction energy.