Read e-book online Applications of the Monte Carlo Method in Statistical PDF

By K. Binder, D. Stauffer (auth.), Professor Dr. Kurt Binder (eds.)

ISBN-10: 3642967884

ISBN-13: 9783642967887

ISBN-10: 3642967906

ISBN-13: 9783642967900

Monte Carlo desktop simulations are actually a regular software in clinical fields akin to condensed-matter physics, together with surface-physics and applied-physics difficulties (metallurgy, diffusion, and segregation, and so forth. ), chemical physics, together with experiences of suggestions, chemical reactions, polymer facts, and so forth. , and box conception. With the expanding skill of this technique to house quantum-mechanical difficulties comparable to quantum spin platforms or many-fermion difficulties, it is going to develop into helpful for different questions within the fields of elementary-particle and nuclear physics in addition. the big variety of contemporary guides dealing both with functions or extra improvement of a few elements of this system is a transparent indication that the medical group has discovered the ability and flexibility of Monte Carlo simula­ tions, in addition to of similar simulation concepts similar to "molecular dynamics" and "Langevin dynamics," that are in basic terms in short pointed out within the current publication. With the expanding availability of contemporary very-high-speed general-purpose desktops, many difficulties develop into tractable that have to this point escaped passable therapy because of prac­ tical barriers (too small platforms needed to be selected, or too brief averaging instances needed to be used). whereas this strategy is basically really pricey, more cost-effective possible choices became on hand, too: (i) array or vector processors specifical­ ly fitted to extensive periods of simulation reasons; (ii) unique objective processors, that are outfitted for a extra particular classification of difficulties or, within the severe case, for the simulation of 1 unmarried version system.

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Extra resources for Applications of the Monte Carlo Method in Statistical Physics

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42]: this means that for any L which are more convenient than the above relation M = lim limL. Similarly, the s p H->O L-iCC> susceptibility can also be estimated in several ways, 2 d . 13) T > Tc lis being the halfwidth of the distribution, or lim«s2> - 2)Ld/ kBT = lim PL2(ML)Ld/(S1TkBT) L-iCC> L-ooo 2 d =lim (lIs)L L-iCO SkBT ln2 = x, T < Tc .

Suzuki, S. Miyashita, A. Kuroda: Progr. Theor. Phys. 58, 701 (1977); S. Miyashita, H. Nishimori, A. Kuroda, M. Suzuki: Progr. Theor. Phys. 28 K. H. Kalos: In Monte Carlo Methods in Statistical Physics, ed. by K. 29 K. 30 K. P. Landau: Phys. Rev. 31 K. Binder: Phys. Rev. Lett. 32 K. Binder: Z. D. Bruce: J. Phys. N. Barber, W. Selke: J. Phys. P. Landau: J. Magn. Mag. Mat. W. Lyklema: Phys. Rev. 36 S. Miyashita: Progr. Teor. Phys. 37 L. Schafer, H. Horner: Z. Phys. 38 H. MUller-Krumbhaar: Z. Phys.

49a]. Here we refrain from giving an exhaustive discussion of this topic, and describe only briefly the thermodynamic integration method, again using Ising magnets as an explicit example. We feel that this method is both simple and versatile, its application is rather straightforward and its usefulness is established by nontrivial examples. The key idea is 23 the fact that F is a function of the thermodynamic state only, as specified by independent thermodynamic variables (T,H for the Ising system), but does not depend on the particular integration path in the space of thermodynamic variables, which is followed reversibly to bring the system from a "reference state" (for which F and S are known) to the desired state.

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Applications of the Monte Carlo Method in Statistical Physics by K. Binder, D. Stauffer (auth.), Professor Dr. Kurt Binder (eds.)

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