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

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

Bargains with the pc simulation of advanced actual sys- tems encounteredin condensed-matter physics and statistical mechanics in addition to in comparable fields comparable to metallurgy, polymer research,lattice gauge conception and quantummechanics.

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18-21) are true not only for the subsystem blocks considered above, but also for finite blocks of size Ld with periodic, free or any other boundary conditions . Note, however, that each boundary condition in finite-size scaling represents a separate "universal i ty . , on the scale L/E,,,,"l boundary effects do not yet cancel out. Of course, the exponents ß,v entering here are the bulk exponents of the infinite system and thus the same for all boundary conditions . 17-21) one recognizes several possibilities to apply finite-size scaling theory to study critical properties.

10) i s not quantitati vely accurate for s""O. g . , H. E. St an1ey : An I n t r oduc t ion to Phase Transitions and Critical Phenomena (University Pr ess , Oxford 1971) D. Stauffer, M. Ferer, M. Wortis: Phys . Rev. Lett . P . R. dos Santos, L. Sneddon : Phys. Rev. 46 K. P. Landau : Phys . Rev . 47 N. E. Fisher : Phys. Rev. L . Cardy, P. Nightinga1e: Phys . Rev . B27, 4256 (1983) Y. Irnry : Phys. Rev. 48 K. Binder: Z. Phys. -K. Ma : J. Stat. Phys. 26, 221 (1981); H. Meirovitch: J. Stat. Phys . 49b O.

I ii) The appropriate choice o f the nwnbe~s "o:" of eonfi gurations used to equi l ibra te and t o avera ge depends on a j udgement of what the e ~aete~stie t imes of a p~ob l ~~ ~e . Aga in l arg e charac te r i sti c t imes occur at phase transit i ons : cri t ical slowing down of fluctuat i ons occurs at se cond-orde r trans iti ons whi le metas ta bil i ty may occur at f i rs t - order t r ansitions. Often i t i s not even possibl e to ma ke the si mu la t ion run lang enough to see the meta s t able st ate actuall y decayi ng t o t he stable one (which is r eac hed by a different choi ce of i nit i al condi t i ons , for i nstance).

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