Dresden 2003 – scientific programme

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DY: Dynamik und Statistische Physik

DY 35: Critical phenomena and phase transitions I

DY 35.3: Talk

Wednesday, March 26, 2003, 15:00–15:15, G\"OR/229

Ferromagnetic ordering in the two-dimensional dipolar xy-model — •Peter Maier and Franz Schwabl — Institut für Theoretische Physik, Physik–Department der Technischen Universität München, James–Franck–Straße, D–85747 Garching, Germany.

We investigate a two-dimensional dipolar xy-model. Without the dipolar interaction the model is known to exhibit the Kosterlitz-Thouless transition, which shows quite unusual critical behavior. Introducing the long-range dipolar forces leads to the appearance of a ferromagnetic phase. Now the question arises whether the new critical point will provide standard critical behavior or if some of the unusual features of the Kosterlitz-Thouless transition will remain at the ferromagnetic transition. From the experimental point of view the dipolar xy-model is interesting as it provides an asymptotic description of the situation in ultrathin magnetic films.

Within the framework of the nonlinear σ-model we predict by means of renormalization group theory a low temperature phase with spontaneous magnetization governed by a low temperature fixed point with infinite dipolar coupling. The critical fixed point shows nonlinear behavior leading to novel critical properties. In particular, the correlation length and the spontaneous magnetization show exponential behavior instead of power laws. Parameterizing the divergencies in terms of the correlation length we calculate the critical exponents.