Prof. Dr. Wolfhard Janke
Institut für Theoretische Physik
Universität Leipzig
Vor dem Hospitaltore 1
D-04103 Leipzig
Postanschrift:
Augustusplatz 10/11
D-04109 Leipzig, Germany
Tel.: (+49) (0)341 9732-725
Sekr.: (+49) (0)341 9732-420 (Frau Voigt)
FAX : (+49) (0)341 9732-548
email:
wolfhard.janke@itp.uni-leipzig.de
Ising Lectures, Lviv, Ukraine, 17 - 20 May 2005
Lectures:
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Introduction to Monte Carlo simulations (Tue, 17.05: 13.30-15.00)
-
Improved algorithms and generalised ensembles (Tue, 17.05: 15.30-17.00)
-
Applications to disordered systems (Thu, 19.05: 15.30-17.00)
Contents:
The aim of this lecture series is to give an overview on the current
state-of-the-art of Monte Carlo computer simulations and to illustrate
them in the first two lectures with simple applications to the Ising model
of statistical physics. After reviewing in the first lecture importance
sampling Monte Carlo schemes based on Markov chains and standard local
update rules such as the Metropolis and heat-bath algorithm, statistical
error analyses of simulation data and critical slowing down at a
second-order phase transition will be discussed. As an important tool for
finite-size scaling analyses, histogram reweighting techniques are
introduced.
Next advanced update algorithms will be considered which,
for certain classes of models, can drastically
improve the performance of simulations. This will be illustrated
with cluster-update algorithms, reducing critical slowing down
at second-order phase transitions, and multicanonical simulations,
greatly improving simulations at first-order phase transitions
and, in general, for systems with rare-event states.
A few other useful methods will be briefly mentioned.
Mainly intended as an outlook, the third lecture
will be devoted to more advanced applications to disordered systems
such as diluted ferromagnets, random lattices and spin glasses
which in general require especially tailored algorithms for their
successful simulation.
Focussing mainly on the basic concepts, the lecture series is addressed
to a broad audience of students, whose main focus may range from applied
to theoretical physics.
Small exercises referring mainly to the first and partly the second
lecture will be assigned, that should be worked out by the students.
Lecture I - Introduction to Monte Carlo simulations
This lecture introduces the basic concepts underlying Monte Carlo
simulations and their statistical analysis. The power of the method
will be illustrated for the Ising model.
-
Importance sampling Monte Carlo
-
Local update procedures (Metropolis, heat-bath)
-
Statistical error analyses (critical slowing down)
-
Histogram reweighting techniques
-
Applications to the Ising model
Lecture II - Improved algorithms and generalised ensembles
For certain classes of models the simulations can be drastically
improved by using more advanced algorithms. This will be illustrated
with cluster-update algorithms, drastically reducing critical slowing down
at second-order phase transitions, and multicanonical simulations,
greatly improving simulations at first-order phase transitions and,
in general, for systems with rare-event states. Other useful methods will
be only briefly mentioned.
-
Cluster algorithms
-
Multigrid methods
-
Generalized ensembles (multicanonical simulations etc.)
-
Simulated and parallel tempering
Lecture III - Applications to disordered systems
Numerical simulations of quenched, disordered systems (e.g.
random-bond or diluted ferromagnets, random lattices or graphs, spin
glasses) in general require especially tailored algorithms in order to
achieve reliable results in reasonable computing times (which are
usually still large, even on supercomputers).
Methodological similarities to the problem of protein folding
will be sketched.
The objective of this lecture is to give an outlook
to computer experiments for such systems and to illustrate them by
specific examples without going too much into the details.
-
Diluted ferromagnets
-
Random lattices or graphs
-
Spin glasses
-
Protein folding
Review articles covering the material of the lectures:
-
W. Janke,
Monte Carlo Simulations of Spin Systems,
invited lecture at the HERAEUS-School ``Physik mit dem
Computer'', Chemnitz, September 18 - 29, 1995, in:
Computational Physics: Selected Methods - Simple Exercises -
Serious Applications, ed. K.H. Hoffmann and M. Schreiber (Springer,
Berlin, 1996), p. 10
[ online].
- W. Janke,
Nonlocal Monte Carlo Algorithms for Statistical Physics
Applications,
Mathematics and Computers in Simulations 47, 329 (1998);
invited review lecture at the IMACS Workshop on
Monte Carlo Methods , Brussels, April 1 - 3, 1997
[ online ].
-
W. Janke,
Pseudo Random Numbers: Generation and Quality Checks,
invited lecture notes, in:
Proceedings of the Euro Winter School Quantum Simulations of
Complex Many-Body Systems: From Theory to Algorithms,
edited by J. Grotendorst, D. Marx, and A. Muramatsu,
John von Neumann Institute for Computing, Jülich,
NIC Series,
Vol. 10, pp. 447-458 (2002)
[
online ].
-
W. Janke,
Statistical Analysis of Simulations: Data Correlations and Error
Estimation,
invited lecture notes, in:
Proceedings of the Euro Winter School Quantum Simulations of
Complex Many-Body Systems: From Theory to Algorithms,
edited by J. Grotendorst, D. Marx, and A. Muramatsu,
John von Neumann Institute for Computing, Jülich,
NIC Series,
Vol. 10, pp. 423-445 (2002)
[
online ].
-
W. Janke,
Multicanonical Monte Carlo Simulations,
Physica A254 , 164 (1998);
invited talk, reprinted in: Proceedings
of StatPhys-Tapei-1997 New Directions in Statistical Physics ,
Academia Sinica, Taipei, Taiwan, August 3 - 11, 1997, eds.
C.-K. Hu and K.-t Leung (Elsevier Science, Amsterdam, 1998); p. 164
[ online ].
-
W. Janke,
Histograms and All That,
in: Computer Simulations of Surfaces and Interfaces,
NATO Science Series, II. Mathematics, Physics and Chemistry - Vol. 114,
Proceedings of the
NATO Advanced Study Institute, Albena, Bulgaria, 9 - 20 September
2002, edited by B. Dünweg, D.P. Landau, and A.I. Milchev
(Kluwer, Dordrecht, 2003), pp. 137 - 157
[ online].
-
W. Janke,
First-Order Phase Transitions,
in: Computer Simulations of Surfaces and Interfaces,
NATO Science Series, II. Mathematics, Physics and Chemistry - Vol. 114,
Proceedings of the
NATO Advanced Study Institute, Albena, Bulgaria, 9 - 20 September
2002, edited by B. Dünweg, D.P. Landau, and A.I. Milchev
(Kluwer, Dordrecht, 2003), pp. 111 - 135
[ online].
-
W. Janke, P.-E. Berche, C. Chatelain, and B. Berche,
Phase Transitions in Disordered Ferromagnets,
in: Proceedings of NIC-Symposium 2004,
Proceedings, edited by D. Wolf, G. Münster, and M. Kremer,
John von Neumann Institute for Computing, Jülich,
NIC Series,
Vol. 20, pp. 241 - 250 (2003)
[
online ].
-
W. Janke and M. Weigel,
Monte Carlo Studies of Connectivity Disorder,
in:
High Performance Computing in Science and Engineering, Munich 2004,
transactions of the Second Joint HLRB and KONWIHR Result and Reviewing
Workshop, March 2nd and 3rd, 2004, Technical University of Munich
(Springer-Verlag, Berlin, Heidelberg, New York, 2004), p. 363 - 373
[ online].
-
W. Janke, B.A. Berg, and A. Billoire,
Multi-Overlap Simulations of Spin Glasses,
in: NIC Symposium 2001,
edited by H. Rollnik and D. Wolf,
John von Neumann Institute for Computing, Jülich,
NIC Series
Vol. 9, pp. 301-314 (2002)
[
online ]
[
cond-mat/0112036].
Recent textbooks on the subject include:
-
M.E.J. Newman and G.T. Barkema,
Monte Carlo Methods in Statistical Physics,
Clarendon Press, Oxford, 1999.
-
D.P. Landau and K. Binder,
Monte Carlo Simulations in Statistical Physics,
Cambridge University Press, Cambridge, 2000.
-
K. Binder and D.W. Heermann,
Monte Carlo Simulations in Statistical Physics: An Introduction,
4th edition,
Springer, Berlin, 2002.
-
B.A. Berg,
Markov Chain Monte Carlo Simulations and Their Statistical Analysis,
World Scientific, Singapore, 2004.
Last Update: Sun May 15 19:34:08 CEST 2005
Last Update: Tue Apr 26 18:38:59 CEST 2005
Last Update: Wed Apr 14 23:44:12 CEST 2005