77,807 research outputs found
Transition Matrix Monte Carlo Method
We analyze a new Monte Carlo method which uses transition matrix in the space
of energy. This method gives an efficient reweighting technique. The associated
artificial dynamics is a constrained random walk in energy, producing the
result that correlation time is proportional to the specific heat.Comment: LaTeX, 8 pages, 1 figur
Self-Learning Monte Carlo Method
Monte Carlo simulation is an unbiased numerical tool for studying classical
and quantum many-body systems. One of its bottlenecks is the lack of general
and efficient update algorithm for large size systems close to phase transition
or with strong frustrations, for which local updates perform badly. In this
work, we propose a new general-purpose Monte Carlo method, dubbed self-learning
Monte Carlo (SLMC), in which an efficient update algorithm is first learned
from the training data generated in trial simulations and then used to speed up
the actual simulation. We demonstrate the efficiency of SLMC in a spin model at
the phase transition point, achieving a 10-20 times speedup.Comment: add more refs and correct some typo
Optimized Monte Carlo Method for glasses
A new Monte Carlo algorithm is introduced for the simulation of supercooled
liquids and glass formers, and tested in two model glasses. The algorithm is
shown to thermalize well below the Mode Coupling temperature and to outperform
other optimized Monte Carlo methods. Using the algorithm, we obtain finite size
effects in the specific heat. This effect points to the existence of a large
correlation length measurable in equal time correlation functions.Comment: Proceedings of "X International workshop on Disordered Systems" held
in Molveno (Italy), March 200
Introduction to the Diffusion Monte Carlo Method
A self-contained and tutorial presentation of the diffusion Monte Carlo
method for determining the ground state energy and wave function of quantum
systems is provided. First, the theoretical basis of the method is derived and
then a numerical algorithm is formulated. The algorithm is applied to determine
the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen
atom, and the electronic ground state of the H2+ ion and of the H2 molecule. A
computer program on which the sample calculations are based is available upon
request.Comment: RevTeX 3.0, 14 pages, 8 EPS figures (included
The Coupled Electron-Ion Monte Carlo Method
In these Lecture Notes we review the principles of the Coupled Electron-Ion
Monte Carlo methods and discuss some recent results on metallic hydrogen.Comment: 38 pages, 6 figures, Lecture notes for the International School of
Solid State Physics, 34th course: "Computer Simulation in Condensed Matter:
from Materials to Chemical Biology", 20 July-1 August 2005 Erice (Italy). To
appear in Lecture Notes in Physics (2006
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