Dresden 2006 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 44: Critical Phenomena and Phase Transitions III

DY 44.5: Vortrag

Donnerstag, 30. März 2006, 15:45–16:00, H\"UL 186

Critical exponents of 3D Ising model from theory and Monte Carlo simulations of very large lattices — •Jevgenijs Kaupuzs — Institute of Mathematics and Computer Science, University of Latvia, LV-1459 Riga, Latvia

We report the results of extended Monte Carlo simulations of 3D Ising model near criticality for linear lattice sizes up to L=640. Our aim is to verify the essentially different predictions for the values of the critical exponents made by the perturbative RG theory [1] and our method of grouping of Feynman diagrams [2]. Our basic method of analysis is to look how the effective critical exponents evaluated either at the critical or at a suitable pseudocritical coupling change with the lattice size. It allows us to control visually the systematic deviations in the results depending on the lattice sizes used in simulations and to evaluate the asymptotic values of the critical exponents by a suitable fit (extrapolation). The usually reported values of the critical exponents appear to be effective rather than asymptotic. Although the currently simulated effective values come closer to the RG ones, the plots of the effective exponents show a tendency to deviate from the RG values towards those found in [2]. We compare this behaviour with that of the effective exponent ν evaluated in [3] from the known experimental data for the superfluid fraction in liquid helium very close to the λ–transition point.

[1] J. Zinn–Justin, Quantum Field Theory and Critical Phenomena, Clarendon Press, Oxford, 1996

[2] J. Kaupužs, Ann. Phys. (Leipzig) 10, 299 (2001)

[3] J. Kaupužs, Eur. Phys. J. B 45, 459 (2005)