Search results for " Statistical Physics"

Monte Carlo simulations of the periodically forced autocatalyticA+B→2Breaction

2000

The one-parameter autocatalytic Lotka-like model, which exhibits self-organized oscillations, is considered on a two-dimensional lattice, using Monte Carlo computer simulations. Despite the simplicity of the model, periodic modulation of the only control parameter drives the system through a sequence of frequency locking, quasiperiodic, and resonance behavior.

Comparison of Monte Carlo simulation and direct multistep scattering theory in (e,e′p) nuclear reactions

1999

Abstract Two methods to deal with final state interactions in (e,e′p) reactions in nuclei are compared. One of them uses a Monte Carlo semiclassical approach while the other uses a statistical quantum mechanical approach. The comparison serves to give support to both approaches, showing at the same time their limitations.

Monte Carlo Simulations of Spin Systems

1996

This chapter gives a brief introduction to Monte Carlo simulations of classical O(n) spin systems such as the Ising (n = 1), XY (n = 2), and Heisenberg (n = 3) models. In the first part I discuss some aspects of the use of Monte Carlo algorithms to generate the raw data. Here special emphasis is placed on nonlocal cluster update algorithms which proved to be most efficient for this class of models. The second part is devoted to the data analysis at a continuous phase transition. For the example of the three-dimensional Heisenberg model it is shown how precise estimates of the transition temperature and the critical exponents can be extracted from the raw data. I conclude with a brief overvi…

Gibbs-ensemble path-integral Monte Carlo simulations of a mixed quantum-classical fluid

1995

We study a model fluid with classical translational degrees of freedom and internal quantum states in two spatial dimensions. The path-integral Monte Carlo and the Gibbs-ensemble Monte Carlo techniques are combined to investigate the liquid-gas coexistence region in this mixed quantum-classical system. A comparison with the phase diagram obtained in the canonical ensemble is also presented.

Phase diagram of a model anticlustering binary mixture in two dimensions: A semi-grand-canonical Monte Carlo study

1994

The temperature-density phase diagram of a model binary mixture in two dimensions is investigated using a semi-grand-canonical Monte Carlo simulation scheme which allows for exchange between the two species while keeping the total number of atoms fixed. The gas-liquid and the gas-solid regions of the phase diagram are mapped out using the efficient block analysis method incorporating finite-size scaling of the various coexisting densities. An ordered square lattice structure is seen to be stable at low temperatures. Interesting short-range ordering phenomena resulting in a ``disorder line'' in the fluid phase are also analyzed and compared with results from liquid-state integral equation th…

HOW MONTE CARLO SIMULATIONS CAN CLARIFY COMPLEX PROBLEMS IN STATISTICAL PHYSICS

2001

Statistical mechanics of condensed matter systems in physics (fluids and solids) derives macroscopic equilibrium properties of these systems as averages computed from a Hamiltonian that describes the atomistic interactions in the system. While analytic methods for most problems involve uncontrolled approximations, Monte Carlo simulations allow numerically exact treatments, apart from statistical errors and from the systematic problem that finite systems are treated rather than the thermodynamic limit. However, this problem can be overcome by finite size scaling methods, and thus Monte Carlo methods have become a very powerful tool to study even complex phase transitions. Examples given wil…

Quantum Monte Carlo Simulations: An Introduction

2002

To be specific, let us consider for the moment the problem of N atoms in a volume V at temperature T, and we wish to calculate the average of some observable A which in quantum mechanics is described by an operator Â.

Monte Carlo renormalization group methods

2014

More on importance sampling Monte Carlo methods for lattice systems

2009

Finite-size tests of hyperscaling.

1985

The possible form of hyperscaling violations in finite-size scaling theory is discussed. The implications for recent tests in Monte Carlo simulations of the d = 3 Ising model are examined, and new results for the d = 5 Ising model are presented.