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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,…
We use the cluster variation method (CVM) to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. The geometrical spin cluster boundaries in these systems serve as models for the string…
The time dependent cluster approximation called the path probability method (PPM) is applied to a pseudo-spin Ising Hamiltonian of the Slater-Takagi model for KH2PO4-type hydrogen-bonded ferroelectrics in order to calculate the homogeneous…
The cluster variation method (CVM) is an approximation technique which generalizes the mean field approximation and has been widely applied in the last decades, mainly for finding accurate phase diagrams of Ising-like lattice models. Here…
The continuous displacement cluster variation method (CDCVM) has introduced local atomic displacements into the theoretical framework of the cluster variation method (CVM) by viewing an atom displaced from a Bravais lattice point as a…
We present a general formalism to make the Replica-Symmetric and Replica-Symmetry-Breaking ansatz in the context of Kikuchi's Cluster Variational Method (CVM). Using replicas and the message-passing formulation of CVM we obtain a…
Cluster variation method (CVM) and path probability method (PPM) have generally been employed to study replacive phase transitions in alloy systems. Recently, displacive phase transitions have been explored within the realm of replacive…
Phase transitions are uncommon among homogenous one-dimensional fluids of classical particles owing to a general non-existence result due to van Hove. A way to circumvent van Hove's theorem is to consider an interparticle potential that is…
The success of the "Cluster Variation Method" (CVM) in reproducing quite accurately the free energies of Monte Carlo (MC) calculations on Ising models is explained in terms of identifying a cancellation of errors: We show that the CVM…
The random--anisotropy Blume--Emery--Griffiths model, which has been proposed to describe the critical behavior of $^3$He--$^4$He mixtures in a porous medium, is studied in the pair approximation of the cluster variation method extended to…
Phase-change materials (PCMs) such as Ge-Sb-Te alloys are widely used in non-volatile memory applications due to their rapid and reversible switching between amorphous and crystalline states. However, their functional properties are…
The path probability method (PPM) in the tetrahedron-cactus approximation is applied to the Slater-Takagi model with dipole-dipole interaction for KH2PO4-type hydrogen-bonded ferroelectric crystals in order to derive a small dip structure…
Despite being invented in 1951 by R. Kikuchi, the 2-D Cluster Variation Method (CVM), has not yet received attention. Nevertheless, this method can usefully characterize 2-D topographies using just two parameters; the activation enthalpy…
Monte Carlo methods are used to study the phase transition in ammonium chloride from the orientationally ordered $\delta$ phase to the orientationally disordered $\gamma$ phase. An effective pair potential is used to model the interaction…
The phase separation behaviors from the single B2 ordered phase into the two separate B2 and L2$_1$ ordered phases in the X-Al-Ti (X: Fe, Co, and Ni) alloys are analyzed using the cluster variation method (CVM) with the interaction energies…
The path probability method (PPM), which is a natural extension of the cluster variation method (CVM) to a time domain, has been employed in a relaxation process of atomic configurations in alloy systems. Although the vacancy mechanism is…
One of the biggest challenges in characterizing 2-D topographies is succinctly communicating the dominant nature of local configurations. In a 2-D grid composed of bistate units, this could be expressed as finding the characteristic…
We present a general framework to study quantum disordered systems in the context of the Kikuchi's Cluster Variational Method (CVM). The method relies in the solution of message passing-like equations for single instances or in the…
The exploration of solid-solid phase transition suffers from the uncertainty of how atoms in two crystal structures match. We devised a theoretical framework to describe and classify crystal-structure matches (CSM). Such description fully…
We exploit the Quantum Cluster Variational Method (QCVM) to study the $J_1$-$J_2$ model for quantum Ising spins. We first describe the QCVM and discuss how it is related to other Mean Field approximations. The phase diagram of the model is…