317 research outputs found
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
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