Related papers: 2-D Cluster Variation Method Free Energy: Fundamen…
A new approach for general artificial intelligence (GAI), building on neural network deep learning architectures, can make use of one or more hidden layers that have the ability to continuously reach a free energy minimum even after input…
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…
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 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…
The proper choice of collective variables (CVs) is central to biased-sampling free energy reconstruction methods in molecular dynamics simulations. The PLUMED 2 library, for instance, provides several sophisticated CV choices, implemented…
The Cluster Variation Method (CVM) is applied to the Ishibashi model for ammonium dihydrogen phosphate ($\rm NH_{4}H_{2}PO_{4}$) of a typical hydrogen bonded anti-ferroelectric crystal. The staggered and the uniform susceptibility without…
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…
We propose clustering algorithms based on a recently developed geometric digraph family called cluster catch digraphs (CCDs). These digraphs are used to devise clustering methods that are hybrids of density-based and graph-based clustering…
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 Cluster Variation Method known in statistical mechanics and condensed matter is revived for weighted bipartite networks. The decomposition of a Hamiltonian through a finite number of components, whence serving to define variable…
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…
Inspired by our earlier semi-stochastic work aimed at converging high-level coupled-cluster (CC) energetics [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017); J. Chem. Phys. 154, 124103 (2021)], we propose a novel…
Exploiting Chemical Short-Range Order (CSRO) is a promising avenue for manipulating the properties of alloys. However, existing modeling frameworks are not sufficient to predict CSRO in multicomponent alloys (>3 components) in an efficient…
It is shown how to derive simple polynomial expressions for the variational configurational entropy starting from the cluster variation method (CVM). As an example, first six terms of the expansion of the entropy in powers of the…
In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes which are then used to compute the energy and other properties. Although it is of…
In this paper, we propose a novel approach for coupling 2D/1D shallow water flow models. Efficiently coupling these models is vital for simulating the flow and flooding of open channels. Currently, existing methods couple the models either…
We consider the approximation of the 2D frictionless contact problem in elasticity using the Virtual Element Methods (VEMs). To overcome the volumetric locking phenomenon in the nearly incompressible case, we adopt a mixed…
Using molecular simulation, we study the nucleation of liquid droplets from binary mixtures and determine the free energy of nucleation along entropic pathways. To this aim, we develop the $\mu_1 \mu_2 VT-S$ method, based on the…
Computing free energy is a fundamental problem in statistical physics. Recently, two distinct methods have been developed and have demonstrated remarkable success: the tensor-network-based contraction method and the neural-network-based…
We propose a practical scheme for one-way quantum computing based on efficient generation of 2D cluster state in thermal cavities. We achieve a controlled-phase gate that is neither sensitive to cavity decay nor to thermal field by adding a…