Abstract
Partition functions and functional integrals (path integrals) reduce many-body problems to complicated multidimensional integrals or sums. Monte Carlo simulations are tools to evaluate in an approximate way these integrals/sums, allowing for fairly precise calculation of observables. The results are exact within statistic and controlled systematic errors. This is a powerful procedure that supplements analytical calculations. A large variety of physical properties can be studied in a wide range of parameters with relatively small effort, allowing the investigation of low, intermediate, and large coupling regimes, where analytical techniques cannot be controlled. The simulations give results that can often be directly compared with experiments, offering a method to determine if a given model contains the essential physics of a system. This allows for a systematic exploration of the relationship between microscopical models and experimental observations, varying the parameters of a model.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
K. Binder, and D.W. Heerman: Monte Carlo Simulation in Statistical Physics ( Springer, Berlin Heidelberg New York 1992 )
K. Binder (Ed.): The Monte Carlo Method in Condensed Matter Physics. Topics Appl. Phys. Vol. 71 ( Springer, Berlin Heidelberg New York 1992 )
J.J. Binney, N.J. Dowrick, A.J. Fisher, and M.E.J. Newman: The Theory of Critical Phenomena, An Introduction to the Renormalization Group ( Oxford Science Pub., Oxford 1993 )
J.W. Negele and H. Orland: Quantum Many-Particle Systems (Addison-Wesley, 1988 )
E. Manousakis: Rev. Mod. Phys. 63, 1 (1991)
N. Metropolis, A. Rosenbluth, M. Rosenbluth, and A. Teller: J. Chem. Phys. 21, 1087 (1953)
Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing (Fortran Numerical Recipes, Vol. 2) W.H. Press et al. (Eds.)
R.H. Swendsen, and J.-S. Wang: Phys. Rev. Lett. 58, 86 (1987)
U. Wolff: Phys. Rev. Lett. 62, 361 (1989)
L. Onsager: Phys. Rev. 65, 117 (1944); B. Kauffman and L. Onsager: Phys. Rev. 76, 1244 (1949)
D.M. Ceperley: Rev. Mod. Phys. 67, 279 (1995); N. Trivedi and D.M, Ceperley: Phys. Rev. B 41, 4552 (1990)
W. von der Linden: A Quantum Monte Carlo Approach to Many-Body Physics,Phys. Rep. 230,53 (1992)
R. Blankenbecler, D.J. Scalapino, and R.L. Sugar: Phys. Rev. D 24, 2278 (1981); J.E. Gubernatis, D.J. Scalapino, R.L. Sugar, and W.D. Toussaint: Phys. Rev. B 32, 103 (1985)
S.R. White, D.J. Scalapino, R.L. Sugar, E.Y. Loh, J.E. Gubernatis, and R.T. Scalettar: Phys. Rev. B 40, 506 (1989)
M. Suzuki: Prog. Theor. Phys. 56, 1454 (1976)
H. Trotter: Proc. Am. Math. Soc. 10, 545 (1959)
R.J. Glauber: J. Math. Phys. 4, 294 (1963)
N. Shibata, K. Ueda: Phys. Rev. B 51, 6 (1995)
J. Zang, H. Röder, A.R. Bishop, and S.A. Trugman: J. Phys. Condens. Matter. 9, L157 (1997)
E. Dagotto, S. Yunoki, A.L. Malvezzi, A. Moreo, J. Hu: Phys. Rev. B 58, 6414 (1998)
J. Riera, K. Hallberg, E. Dagotto: Phys. Rev. Lett. 79, 713 (1997) 7.22 P. Gambardella et al.: Nature 416, 301 (2002)
A. Auerbach: Interacting Electrons and Quantum Magnetism ( Springer, Berlin Heidelberg New York 1994 )
N.D. Mermin and H. Wagner: Phys. Rev. Lett. 17, 1133 (1966)
E. Manousakis: Rev. Mod. Phys. 63, 1 (1991)
I. Affleck, T. Kennedy, E.H. Lieb and H. Tasaki: Commun. Math. Phys. 115, 477 (1988)
J. Frolich, R. Israel, E.H. Lieb and B. Simon: Commun. Math. Phys. 62, 1 (1978)
H. Nakano and M. Takahashi: Phys. Rev. B 52, 6606 (1995)
B.S. Shastry: Phys. Rev. Lett. 60, 639 (1988)
F.D.M. Haldane: Phys. Rev. Lett. 60, 635 (1988)
F.J. Dyson: Commun. Math. Phys. 21, 269 (1971)
B. Simon: J. Stat. Phys. 26, 307 (1981)
R.B. Griffiths: Phys. Rev. 136A, 327 (1964)
L. Onsager: Phys. Rev. 65, 117 (1944)
D. Knuth, The Art of Computer Programming (Addison-Wesley, 1973 )
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Alvarez, G., Feiguin, A. (2003). Monte Carlo Simulations and Application to Manganite Models. In: Nanoscale Phase Separation and Colossal Magnetoresistance. Springer Series in Solid-State Sciences, vol 136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05244-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-662-05244-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07753-1
Online ISBN: 978-3-662-05244-0
eBook Packages: Springer Book Archive