Berlin 2005 – scientific programme

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DY: Dynamik und Statistische Physik

DY 50: Critical Phenomena and Phase Transitions

DY 50.10: Talk

Wednesday, March 9, 2005, 12:15–12:30, TU H3010

Critical Exponents of 3D Ising Model: Theory and Large–Scale Monte Carlo Simulations — •Jevgenijs Kaupužs — Univ. Latvia, LV–1459 Riga, Latvia

It is widely believed that the critical exponents of 3D lattice spin models are accurately predicted by the perturbative renormalization group (RG) theory [1]. An alternative analytical method has been developed in [2], where the perturbative RG theory has been critised and the set of possible exact values of the critical exponents for O(n) models has been proposed.

Recently [3] some Monte Carlo simulations of 3D Ising model on unusually large lattices (with linear lattice size up to L=410) very close to the critical point have been performed to verify the critical exponents.

We have improved the accuracy of our previous simulations and have extended them to L=512. The magnetization at reduced temperatures t ∼ 0.00006 have been considered. It shows that the critical exponent β deviates above the RG value 0.326 towards our [2] asymptotic value 3/8 when approaching the critical point. Generally, our results provide some arguments in favour of the theory developed in [2] and show that previous simulations by Hasenbusch and others relatively far away from criticality give effective rather than asymptotic values of the critical exponents.

[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, Proceedings of SPIE 5471, 480 (2004)