Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 42: Critical Phenomena and Phase Transitions

DY 42.10: Talk

Friday, March 18, 2011, 12:30–12:45, ZEU 255

Optimizing Wilson’s Momentum Shell Renormalization Group — •Andreas Troester — Johannes Gutenberg University, Mainz, Germany

Previous attempts to accurately compute critical exponents from Wilson’s momentum shell renormalization prescription suffered from the difficulties posed by the presence of an infinite number of irrelevant couplings. Taking the example of the 1d long-ranged Ising model [A. Tröster, PRE 79, 036707 (2009)], we calculate the momentum shell renormalization flow in the plane spanned by the coupling constants (u₀,r₀) by a simulation method based on our recently developed Fourier Monte Carlo algorithm [A. Tröster, PRB 76, 012402 (2007); PRL 100, 140602 (2008); Comput. Phys. Comm. 179, 30 (2008)]. Carrying out such simulations for different values of the momentum shell thickness parameter b, we report strong anomalies in the b-dependence of the fixed point couplings and the resulting exponents y_τ and ω in the vicinity of a shell parameter b^*<1 characterizing a thin but finite momentum shell. Evaluation of the exponents for this "optimized" value b^* of b yields a dramatic improvement of their numerical accuracy, indicating a strong damping of the influence of irrelevant couplings [A. Tröster, Phys. Rev. B 81, 125135 (2010); Comput. Phys. Comm., accepted for publication (2010)].