Monte carlo techniques

Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring probability density functions.     

Monte carlo study of anSU(2) lattice gauge-Higgs theory at finite temperature

AnSU(2) gauge theory coupled to a Higgs field in the fundamental representation is studied at finite temperature by Monte Carlo method. Calculations are done on 8⁴, 8³×4 and 8³×2 lattices with a small Higgs self-coupling constant. In the parameter region we studied both the location and the order of the Higgs transition are found to be insensitive to the system's temperature. As for the deconfining transition at finite temperature, our data suggest that it disappears within the symmetric region as the Higgs bare mass decreases. Results on the Higgs energy density and the gauge energy density are also presented.     

Monte carlo simulations of microemulsions

Summary We describe the Larson-Stauffer model of a microemulsion and report results which strongly indicate that this is a successful model. Particular attention is paid to the structure of the surfactant which appears to be the decisive factor for modelling a microemulsion. We study the kinetics of micelle formation, the miscibility gap of oil and water, the coexistence of various phases, the segregation of three phases (oil rich, water rich and the bicontinuous surfactant rich) as a function of temperature, the relative interaction strengths of hydrophobic and hydrophilic monomers of the surfactant with oil and water, and concentration of surfactant. The model is capable of describing most of the observed properties of a microemulsion. In addition, we are now in the position to study the properties of ?designer? surfactant,e.g., ?bola-form?. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Monte carlo estimates of domain-deformation sensitivities

It is shown that, when a Monte Carlo algorithm is used for estimation of any physical quantity A, a simple and fast additional procedure can be implemented that simultaneously estimates the sensitivity of A to any problem parameter. The proposed approach is general and systematic in the sense that: (i) it includes domain-deformation sensitivities, i.e., cases where a change in the parameter modifies the domain over which the sampled random variables are defined and (ii) a simple generic procedure is presented to address all remaining free choices in terms of variance minimization.     

Monte carlo simulation of a quantized universe

A Monte Carlo simulation method which yields groundstate wave functions for multielectron atoms is applied to quantized cosmological models. In quantum mechanics, the propagator for the Schrödinger equation reduces to the absolute value squared of the groundstate wave function in the limit of infinite Euclidean time. The wave function of the universe as the solution to the Wheeler-DeWitt equation may be regarded as the zero energy mode of a Schrödinger equation in coordinate time. The simulation evaluates the path integral formulation of the propagator by constructing a large number of paths and computing their contribution to the path integral using the Metropolis algorithm to drive the paths toward a global minimum in the path energy. The result agrees with a solution to the Wheeler-DeWitt equation which has the characteristics of a nodeless groundstate wave function. Oscillatory behavior cannot be reproduced although the simulation results may be physically reasonable. The primary advantage of the simulations is that they may easily be extended to cosmologies with many degrees of freedom. Examples with one, two, and three degrees of freedom (d.f.) are presented.This essay was awarded Honorable Mention by the Gravity Research Foundation.Part of this work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract number W-7405-ENG-48 and part was supported by National Science Foundation Grant PHY82-13411 to Oakland University.     

Monte carlo calculations of the conformal charge

The conformal charge is an important quantity which characterizes the nature of the two-dimensional phase transition. We report a first attempt to use a new numerical method to calculate the conformal charge. In this paper, we apply our method to the 2-dimensional, ⁴, continuous-spin Ising model. By varying the parameters in the Hamiltonian, one can change continuously from the known Gaussian limit to the Ising limit. It is well known that the critical points for these two systems are not in the same universality class. We study this behavior for the Gaussian model, the single-well ⁴ model, the border model, and the double-well ⁴ model for a large lattice. Our results, while giving a good general picture, are not so far sufficient to differentiate whether the non-Gaussian cases studied belong to the Ising model universality class or not. Further studies of other lattice sizes should serve to improve greatly our conclusions.     

Monte carlo calculations near a uniaxial Lifshitz point

The Monte Carlo method is applied to a threedimensional Ising model with nearest neighbour ferromagnetic interactions and next nearest neighbour antiferromagnetic interactions along one axis only. Special emphasis is given to the critical behaviour near the Lifshitz point.Some parts of this paper have been presented at the 13th International Conference on Statistical Physics, Haifa, August 1977     

Monte carlo study of a hard x-ray concentrator

Summary The sensitivity limits of hard X-ray (> 10 keV) detectors of the current generation are reviewed and the need for a new generation of instruments based on photon concentration is justified. A hard X-ray concentrator based on Bragg diffraction technique is proposed. Such an instrument has been simulated with Monte Carlo methods and the expected performances of a particular configuration are evaluated. The proposed instrument concept is shown to be very promising in the energy range from 10 keV up to about 80 keV. To speed up publication, the proofs were not sent to the authors and were supervised by the Scientific Committee.     

Monte carlo study of coulombic criticality in polyelectrolytes

The role of charges in determining the water solubility of polyelectrolytes, a question of considerable relevance to biology, is currently unresolved. We use computer simulations to study the purely Coulombic phase separation of flexible polyelectrolytes with monovalent counterions in an athermal solvent. In agreement with recent theories we find that the critical temperature for this transition increases with chain length, but that the critical density remains unchanged. We therefore stress that the phase behavior of polyelectrolytes is qualitatively different from uncharged polymers, where the critical density decreases towards zero for long chains.     

Monte carlo simulations of carrier transport and relaxation in superlattices

Monte Carlo simulations of carrier transport through an undoped superlattice into an extended well are described. The results illustrate clearly the important role played by LO phonons in relaxing the energy and the desirability of designing structures which minimize the need for acoustic phonon participation. Attention is drawn to the fact that although, for the standard structures investigated, the LO phonon relaxation rate is relatively independent of the miniband and/or the quantum well eigenstates, the precise shape of the form-factor for an allowed LO transition could play an important role in deciding the relative number of 'slow' carriers in an actual system.     

Monte carlo simulation of channeling effects on recoil motion

Using a Monte Carlo simulation method we have investigated the channeled motion of recoils in a composite amorphous-crystalline target. The study has been applied to a SiO₂/Si system and to the motion of oxygen recoils in the crystalline Si substrate.     

Monte carlo simulation of mixing of a multilayered target

This work presents a Monte Carlo simulation of ion mixing of a multilayered target. The simulation deals with collisional effects and accounts for the dynamic alteration of the target under ion bombardment. The results refer to As implants, 190 keV, on a target composed of alternating Ni-Ta layers on a Si substrate.     

Monte carlo simulation of magnetization and coercivity of free magnetic clusters

Based on Monte Carlo method, the oscillatory behaviour of the average magnetic moment as a function of the cluster sizes and the temperature dependences of magnetic moment with different sizes have been studied. It is found that the oscillations superimposed on the decreasing moment are associated with not only the geometrical structure effects but also the thermal fluctuation. The hystereses and thermal coercivities for free clusters with zero and finite uniaxial anisotropies have been calculated. The simulated thermal dependence of the coercivity is consistent with the experimental result, but does not fit the T^α law in the whole temperature range. It is evident that an easy magnetization direction and an anisotropy resulting from the spin configurations exist in the free clusters with the pure exchange interaction, which is also proved by the natural angle and energy distribution of clusters. A systematic theoretical analysis is also made to establish the relationship between natural angle and coercivity.     

Size effects in triplet-triplet annihilation: II. Monte carlo simulations

The dynamics of triplet-triplet annihilation (TTA) is theoretically studied in linear chains and nanoparticles, modeled as 1D, 2D, and 3D regular lattices, as a function of size M, of the rate of excitation migration W, and of the rate of excitation annihilation V in the diffusion-influenced limit (V ≫ W). It is shown that a sum of two exponentials is usually sufficient for fitting experimental phosphorescence and triplet-triplet absorption decays. The first term describes the decay of domains containing initially one triplet, while the second one reflects the disappearance of domains containing initially two triplets. Monte Carlo calculations were carried out to compute the survival probability of an annihilating pair of triplets, yielding expressions for the dependence of the rate constant of TTA on the parameters M, W, and V in one, two, and three dimensions. The text was submitted by the authors in English.     

Monte carlo simulations of the two-dimensional two-component plasma on a line

We study by means of Monte Carlo simulations the Kosterlitz-Thouless transition for the two-dimensional, two-component plasma confined on a line.