A Variational Approach to Monte Carlo Renormalization Group

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The 2D Ising model is used to illustrate the method.Comment: 4 pages, 3 figures, 1 tabl

A Variational Approach to Monte Carlo Renormalization Group

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The 2D Ising model is used to illustrate the method.Comment: 4 pages, 3 figures, 1 tabl

Monte Carlo Renormalization Group for Systems with Quenched Disorder

We extend to quenched disordered systems the variational scheme for real space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow of the renormalized Hamiltonian distribution, from which one can compute the critical exponents if the correlations of the renormalized couplings retain finite range. Key to the variational approach is the bias potential found by minimizing a convex functional in statistical mechanics. This potential reduces dramatically the Monte Carlo relaxation time in large disordered systems. We demonstrate the method with applications to the two-dimensional dilute Ising model, the random transverse field quantum Ising chain, and the random field Ising in two and three dimensional lattices

Phase equilibrium of liquid water and hexagonal ice from enhanced sampling molecular dynamics simulations

We study the phase equilibrium between liquid water and ice Ih modeled by the TIP4P/Ice interatomic potential using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice Ih-liquid free energy differences from simulations that visit reversibly both phases. The reversible interconversion is achieved by introducing a static bias potential as a function of an order parameter. The order parameter was tailored to crystallize the hexagonal diamond structure of oxygen in ice Ih. We analyze the effect of the system size on the ice Ih-liquid free energy differences and we obtain a melting temperature of 270 K in the thermodynamic limit. This result is in agreement with estimates from thermodynamic integration (272 K) and coexistence simulations (270 K). Since the order parameter does not include information about the coordinates of the protons, the spontaneously formed solid configurations contain proton disorder as expected for ice Ih.Comment: 9 pages, 6 figure

In situ Characterization of Nanoparticles Using Rayleigh Scattering

We report a theoretical analysis showing that Rayleigh scattering could be used to monitor the growth of nanoparticles under arc discharge conditions. We compute the Rayleigh scattering cross sections of the nanoparticles by combining light scattering theory for gas-particle mixtures with calculations of the dynamic electronic polarizability of the nanoparticles. We find that the resolution of the Rayleigh scattering probe is adequate to detect nanoparticles as small as C60 at the expected concentrations of synthesis conditions in the arc periphery. Larger asymmetric nanoparticles would yield brighter signals, making possible to follow the evolution of the growing nanoparticle population from the evolution of the scattered intensity. Observable spectral features include characteristic resonant behaviour, shape-dependent depolarization ratio, and mass-dependent line shape. Direct observation of nanoparticles in the early stages of growth with unobtrusive laser probes should give insight on the particle formation mechanisms and may lead to better-controlled synthesis protocols

A well-scaling natural orbital theory

We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree-Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the one-particle density matrix.Comment: http://www.pnas.org/cgi/doi/10.1073/pnas.1615729113. arXiv admin note: text overlap with arXiv:1309.392