Search results for "Dynamic Monte Carlo method"
showing 10 items of 83 documents
Medium-range interactions and crossover to classical critical behavior
1996
We study the crossover from Ising-like to classical critical behavior as a function of the range R of interactions. The power-law dependence on R of several critical amplitudes is calculated from renormalization theory. The results confirm the predictions of Mon and Binder, which were obtained from phenomenological scaling arguments. In addition, we calculate the range dependence of several corrections to scaling. We have tested the results in Monte Carlo simulations of two-dimensional systems with an extended range of interaction. An efficient Monte Carlo algorithm enabled us to carry out simulations for sufficiently large values of R, so that the theoretical predictions could actually be …
Critical phenomena without “hyper scaling”: How is the finite-size scaling analysis of Monte Carlo data affected?
2010
Abstract The finite size scaling analysis of Monte Carlo data is discussed for two models for which hyperscaling is violated: (i) the random field Ising model (using a model for a colloid-polymer mixture in a random matrix as a representative) (ii) The Ising bi-pyramid in computing surface fields.
Path-integral Monte Carlo study of crystalline Lennard-Jones systems.
1995
The capability of the path-integral Monte Carlo (PIMC) method to describe thermodynamic and structural properties of solids at low temperatures is studied in detail, considering the noble-gas crystals as examples. In order to reduce the systematic limitations due to finite Trotter number and finite particle number we propose a combined Trotter and finite-size scaling. As a special application of the PIMC method we investigate $^{40}\mathrm{Ar}$ at constant volume and in the harmonic approximation. Furthermore, isotope effects in the lattice constant of $^{20}\mathrm{Ne}$ and $^{22}\mathrm{Ne}$ are computed at zero pressure. The obtained results are compared with classical Monte Carlo result…
Cluster Expansions and Variational Monte Carlo in Medium Light Nuclei
1993
The B1 Brink-Boeker effective interaction is used to compute variational upper bounds for the ground state energy of nuclei from 16 O up to 40 Ca. The calculations are carried out by means of the Variational Monte Carlo method and with a multiplicative cluster expansion up to fourth order.
Molecular-Level Characterization of Heterogeneous Catalytic Systems by Algorithmic Time Dependent Monte Carlo
2009
Monte Carlo algorithms and codes, used to study heterogeneous catalytic systems in the frame of the computational section of the NANOCAT project, are presented along with some exemplifying applications and results. In particular, time dependent Monte Carlo methods supported by high level quantum chemical information employed in the field of heterogeneous catalysis are focused. Technical details of the present algorithmic Monte Carlo development as well as possible evolution aimed at a deeper interrelationship of quantum and stochastic methods are discussed, pointing to two different aspects: the thermal-effect involvement and the three-dimensional catalytic matrix simulation. As topical app…
Guide to Practical Work with the Monte Carlo Method
2002
The guide is structured such that we proceed from the “easy” simulation methods and algorithms to the more sophisticated. For each method the algorithms are presented by the technique of stepwise refinement. We first present the idea and the basic outline. From then on we proceed by breaking up the larger logical and algorithmic structures into smaller ones, until we have reached the level of single basic statements. Sometimes we may elect not to go to such a depth and the reader is asked to fill in the gaps.
On the adoption of the Monte Carlo method to solve one-dimensional steady state thermal diffusion problems for non-uniform solids
2013
Abstract The present paper is focussed on the investigation of the potential adoption of the Monte Carlo method to solve one-dimensional, steady state, thermal diffusion problems for continuous solids characterised by an isotropic, space-dependent conductivity tensor and subjected to non-uniform heat power deposition. To this purpose the steady state form of Fourier’s heat diffusion equation relevant to a continuous, heterogeneous and isotropic solid, undergoing a space-dependent heat power density has been solved in a closed analytical form for the general case of Cauchy’s boundary conditions. The thermal field obtained has been, then, put in a peculiar functional form, indicating that it …
On the Ground State Structure of Adsorbed Monolayers: Can One Find them by Monte Carlo Simulation?
2002
While the classical ground state structure of an atomic monolayer adsorbed at a noncorrugated perfectly flat substrate trivially is a triangular lattice, the spacing being the minimum of the interatomic potential, nontrivial structures occur on corrugated substrates. This problem is exemplified for the (100) face of a face-centered cubic crystal, varying both the density of the adsorbed monolayer and the strength of the potential due to the surface. Increasing the density beyond that of the commensurate c(2 x 2) structure, incommensurate patterns become stable with “heavy” walls (HW) oriented along the face diagonals [including the “crossing heavy walls” (CRHW) phase]. It is shown that slow…
Capillary condensation in the two-dimensional lattice gas: A Monte Carlo test of fluctuation corrections to the Kelvin equation
1997
A two-dimensional lattice gas model with nearest-neighbour attractive interaction confined in a strip of width L between two parallel boundaries at which an attractive short-range force acts is studied by Monte Carlo simulations, for cases where the system is in the wet phase near the critical wetting transition line for . We study the shift of the chemical potential of the transition in the strip as a function of L by thermodynamic integration methods, , and also obtain the thickness of the wetting film at the chemical potential at which capillary condensation occurs. In the range the data are consistent with a variation according to the Kelvin equation, , as well as with a shifted Kelvin …
Structural properties ofSi1−xGexalloys: A Monte Carlo simulation with the Stillinger-Weber potential
1995
The structural properties of binary silicon-germanium alloys are investigated by means of large-scale constant-pressure Monte Carlo simulations of the Stillinger-Weber model. At low temperatures, the binary-mixture phase separates into Si-rich and Ge-rich phases. The two-phase coexistence region is terminated by a critical point that belongs to the mean-field universality class. We also studied the structural properties of pure Si and Ge as well as the binary mixture. In particular, we found that the linear thermal expansions for both Si and Ge are in agreement with experiments, and that V\'egard's law is valid at temperatures above the critical point. Finally, we compare the bond-length an…