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

An anomalous alloy: Y_x Si_{1-x}

We study via density functional-based molecular dynamics the structural and dynamical properties of the rare earth silicon amorphous alloy Y_xSi_{1-x} for x=0.093 and x=0.156. The Si network forms cavities in which a Y^{3+} cation is entrapped. Its electrons are transferred to the Si network and are located in the dangling bonds of the Si atoms that line the Y cavities. This leads to the presence of low coordinated Si atoms that can be described as monovalent or divalent anions. For x=0.156, the cavities touch each other and share Si atoms that have two dangling bonds. The vibrational spectrum is similar to that of amorphous Si. However, doping induces a shoulder at 70 cm^{-1} and a pronounced peak at 180 cm^{-1} due to low coordinated Si.Comment: 4 pages, 4 figure