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 Dr. Arnaud Buhot
[email][www]
SPrAM, INAC, CEA Grenoble. Phone +33 4 38 78 38 68

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With the advent of computers it became possible to carry out
simulations of models which were intractable using `classical'
theoretical techniques. In many cases computer have, for the first
time in history, enable physicists not only to invent new models for
various aspects of nature but also to solve those same models without
substantial simplification. In recent years computer power has
increased quite dramatically, with access to computers becoming both
easier and more common (e.g. with personal computers and
workstations), and computer simulation methods have also been steadily
refined. As a result computer simulations have become another way of
doing physics research. They provide another perspective, in some
cases simulations provide a theoretical basis for understanding
experimental results, and in other instances simulations provide
`experimental' data with which theory may be compared.
This 67 lecture course is intended to introduce graduate students to
numerical simulations in condensed matter. Special emphasis will be
given to the physics of the numerical algorithms and a vast range
of problems will be covered.
It will be assumed that students have a previous knowledge of
statistical mechanics. Some previous experience in programming is
needed. For those students who have not (or have forgot) basic
programming skills, a zerolecture about FORTRAN programming
will be held.
At the end of the course students are encouraged to develop a project
under supervision

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If necessary a brief introduction to programming in FORTRAN will
be given before the course
 Introduction to FORTRAN programming
 Central Limit Theorem.
 Fortran background (variable, operators, functions, Input/Output...).
 Random number generators.
In the main body of the course, it is hoped that the following
topics will be covered:
 Some necessary background
 A quick reminder in thermodynamics and statistical mechanics.
 1D Ising Model.
 Finite size scaling.
 Fluctuations and errors.
 Equilibrium Monte Carlo Simulations
 Ising Model.
 Important sampling.
 Metropolis, Glauber and Kawasaky algorithms.
 Cluster methods.
 Multicanonical methods.
 Nonequilibrium Monte Carlo Simulations
 Directed percolation.
 Kinetically constrained models.
 Continuous time Monte Carlo.
 Offlattice simulations
 Hard sphere problems.
 Cluster algorithms.
 Molecular dynamics.
 Langevin Dynamics
 Brownian motion.
 Model A, model B, etc. equations.
 KardarParisiZhang equation.
 Numerical simulation of stochastic differential equations.
 Projects

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 K. Binder and D. W. Heermann,
Monte Carlo Simulation in Statistical Physics.
An introduction.
SpringerVerlag, Berlin (1988).
 D. P. Landau and K. Binder,
A guide to Monte Carlo Simulations in Statistical
Physics,
Cambridge University Press (2000).
 M. E. J. Newman and G. T. Barkema,
Monte Carlo Methods in Statistical Physics,
Clarendon Press, Oxford (1999).
 C. W. Gardiner,
Handbook of Stochastic Methods,
SpringerVerlag, Berlin, (1997).
 Daan Frenkel and Berend Smit,
Understanding Molecular Simulation: From Algorithms to
Applications,
Academic Press Boston (1996).
 Werner Krauth,
Introduction to Monte Carlo Algorithms,
43 pages [pdf]
 K. P. N. Murthy,
Introduction to Monte Carlo Simulation of Statistical
Physics problems,
45 pages [pdf]

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Handbooks
 Introduction to Fortran, Aleksandar Donev, 31 pages
[pdf,ps]
 Professional Programmers's Guide to Fortran 77,
Clive G. Page, 122 pages [ps]
Document files are in Postscript format
 0th Lecture:
Background in Fortran and Central Limit Theorem
 1st Lecture:
Background in thermodynamics and 1D Ising Model
 2nd Lecture:
Equilibrium MonteCarlo simulations and 2D Ising model
 3rd Lecture:
Nonequilibrium MonteCarlo simulations : directed
percolation and kinetically constrained models
 4th Lecture:
Offlattice simulations : cluster algorithm and molecular
dynamics
 5th Lecture:
Langevin dynamics and KPZ dynamics
Notes on the 2nd Lecture
Codes
Some codes are in ASCII format.
Ask A. Buhot
for the remaining ones but try to make your own ones
before
 0th Lecture
 clt.f: Central Limit Theorem verification
 moment.f: moment calculation subroutine
 1st Lecture
 ising1d.f: 1D Ising model (calculate
the partition function)
 eval.f: energy evaluation subroutine
 2nd Lecture
 ising.f: 2D Ising model with
Glauber/Metropolis dynamics
 kawa.f: 2D Ising model with Kawasaki
dynamics
 wolff.f: 2D Ising model with Wolff
algorithm
 3rd Lecture
 dptrivial.f: 1D Directed Percolation using
trivial Monte Carlo algorithm
 dpwrong.f: 1D Directed Percolation using
wrong continuous time Monte Carlo
 dpright.f: 1D Directed Percolation using
correct continuous time Monte Carlo
 dpwrong.eps: Comparison of the three MonteCarlo
algorithms
 resp.f: FluctuationDissipation Relations
in the 1D Constrained Ising chain.
 resp.dat: Contains the common
variables for resp.f
 4th Lecture
 cluster.f: 2D monodisperse hard square
model using the cluster algorithm.
 cluster.dat: Contains the common
variables for cluster.f
 init.f: Create an initial condition for the
2D monodisperse hard square model.
 visu.f: Create a postscript file to
visualise the squares
 5th Lecture
 ou.f: Simulate the OrnsteinUhlenbeck
process.
 ma.f: Simulate the x^2+x^4 theory using
Model A dynamics
 mb.f: Simulate the x^2+x^4 theory using
Model B dynamics
 kpz.f: Simulate the KPZ equition in 1D.
