Gießen 2007 – scientific programme

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HK: Fachverband Physik der Hadronen und Kerne

HK 14: Theorie

HK 14.9: Talk

Tuesday, March 13, 2007, 16:15–16:30, C

Critical exponents and finite size scaling from non-perturbative Renormalization Group methods — •Bertram Klein¹ and Jens Braun² — ¹Physik Department, Technische Universität München, 85747 Garching — ²Institut für Theoretische Physik, Universität Heidelberg, 69120 Heidelberg

Continuous phase transitions and critical behavior are characterized by the appearance of long-range fluctuations. These critical fluctuations give rise to universal behavior that is independent of the dynamics of the underlying system and can be studied in much simpler model systems in the same universality class.

For the investigation of the phase transition in Quantum Chromodynamics, lattice simulations are indispensable. However, they are still restricted to relatively large quark masses and small volumes. To determine the order of the phase transition, a scaling analysis is an important tool. It requires reliable knowledge of critical exponents, scaling functions and finite size scaling effects. Renormalization Group (RG) methods have been very successful in providing this knowledge.

We apply non-perturbative RG methods to an O(N)-model in a finite 3-dimensional volume and consider explicit breaking of the symmetry. Our goal is to obtain critical exponents and to investigate the effects of the finite volume, which acts as an infrared-cutoff for the long-range fluctuations and affects the critical behavior. We obtain results for critical exponents and the deviation of the scaling from the infinite volume behavior.