Regensburg 1998 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 53: Phasenübergänge und kritische Phänomene

DY 53.1: Vortrag

Freitag, 27. März 1998, 10:30–10:45, H2

Finite-size scaling in the ϕ⁴ theory above the upper critical dimension — •X.S. Chen^1,2 and V. Dohm¹ — ¹Institut für Theoretische Physik, RWTH Aachen, 52056 Aachen — ²Institute of Particle Physics, Hua-Zhong Normal University, Wuhan, China

We demonstrate that the standard O(n) symmetric ϕ⁴ field theory does not correctly describe the leading finite-size effects near the critical point of spin systems on a d-dimensional lattice with d > 4 [1]. On the basis of exact results for n → ∞ and of one-loop results for finite n we show that the widely accepted lowest-mode approach [2] fails for the ϕ⁴ field theory above the upper critical dimension [1,3]. For the field-theoretic model, the free energy for d > 4 is shown to have a nonuniversal finite-size scaling structure with two reference lengths. For a ϕ⁴ lattice model, universal finite-size scaling functions with two reference lengths are calculated. These results are relevant to as yet unexplained Monte-Carlo data of d=5 Ising model [4].

Gefördert von der Deutschen Forschungsgemeinschaft (SFB 341)

[1] X.S. Chen, V. Dohm, submitted to Phys. Rev. Lett. (Sept. 1997)

[2] E. Brézin, J. Zinn-Justin, Nucl. Phys. B257 [FS14], 867 (1985)

[3] X.S. Chen, V. Dohm, submitted to Eur. Phys. J. B (Oct. 1997)

[4] Ch. Rickwardt, P. Nielaba, K. Binder, Ann. Phys. (Leipzig) 3, 483 (1994)