2,523 research outputs found
Computer simulation of two continuous spin models using Wang-Landau-Transition-Matrix Monte Carlo Algorithm
Monte Carlo simulation using a combination of Wang Landau (WL) and Transition
Matrix (TM) Monte Carlo algorithms to simulate two lattice spin models with
continuous energy is described. One of the models, the one dimensional
Lebwohl-Lasher model has an exact solution and we have used this to test the
performance of the mixed algorithm (WLTM). The other system we have worked on
is the two dimensional XY-model. The purpose of the present work is to test the
performance of the WLTM algorithm in continuous models and to suggest methods
for obtaining best results in such systems using this algorithm.Comment: 29 pages, 15 figure
A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State Spaces
Advanced algorithms are necessary to obtain faster-than-real-time dynamic
simulations in a number of different physical problems that are characterized
by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms
that preserve the dynamics of the model are described. These include the
-fold way algorithm, the Monte Carlo with Absorbing Markov Chains (MCAMC)
algorithm, and the Projective Dynamics (PD) algorithm. To demonstrate the use
of these algorithms, they are applied to some simplified models of dynamic
physical systems. The models studied include a model for ion motion through a
pore such as a biological ion channel and the metastable decay of the
ferromagnetic Ising model. Non-trivial parallelization issues for these dynamic
algorithms, which are in the class of parallel discrete event simulations, are
discussed. Efforts are made to keep the article at an elementary level by
concentrating on a simple model in each case that illustrates the use of the
advanced dynamic Monte Carlo algorithm.Comment: 53 pages, 17 figure
Transition matrix Monte Carlo method for quantum systems
We propose an efficient method for Monte Carlo simulation of quantum lattice
models. Unlike most other quantum Monte Carlo methods, a single run of the
proposed method yields the free energy and the entropy with high precision for
the whole range of temperature. The method is based on several recent findings
in Monte Carlo techniques, such as the loop algorithm and the transition matrix
Monte Carlo method. In particular, we derive an exact relation between the DOS
and the expectation value of the transition probability for quantum systems,
which turns out to be useful in reducing the statistical errors in various
estimates.Comment: 6 pages, 4 figure
Teaching statistical physics by thinking about models and algorithms
We discuss several ways of illustrating fundamental concepts in statistical
and thermal physics by considering various models and algorithms. We emphasize
the importance of replacing students' incomplete mental images by models that
are physically accurate. In some cases it is sufficient to discuss the results
of an algorithm or the behavior of a model rather than having students write a
program.Comment: 21 pages, 4 figures, submitted to the American Journal of Physic
Computing quantum phase transitions
This article first gives a concise introduction to quantum phase transitions,
emphasizing similarities with and differences to classical thermal transitions.
After pointing out the computational challenges posed by quantum phase
transitions, a number of successful computational approaches is discussed. The
focus is on classical and quantum Monte Carlo methods, with the former being
based on the quantum-to classical mapping while the latter directly attack the
quantum problem. These methods are illustrated by several examples of quantum
phase transitions in clean and disordered systems.Comment: 99 pages, 15 figures, submitted to Reviews in Computational Chemistr
Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
We describe an efficient Monte Carlo algorithm using a random walk in energy
space to obtain a very accurate estimate of the density of states for classical
statistical models. The density of states is modified at each step when the
energy level is visited to produce a flat histogram. By carefully controlling
the modification factor, we allow the density of states to converge to the true
value very quickly, even for large systems. This algorithm is especially useful
for complex systems with a rough landscape since all possible energy levels are
visited with the same probability. In this paper, we apply our algorithm to
both 1st and 2nd order phase transitions to demonstrate its efficiency and
accuracy. We obtained direct simulational estimates for the density of states
for two-dimensional ten-state Potts models on lattices up to
and Ising models on lattices up to . Applying this approach to
a 3D spin glass model we estimate the internal energy and entropy at
zero temperature; and, using a two-dimensional random walk in energy and
order-parameter space, we obtain the (rough) canonical distribution and energy
landscape in order-parameter space. Preliminary data suggest that the glass
transition temperature is about 1.2 and that better estimates can be obtained
with more extensive application of the method.Comment: 22 pages (figures included
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