Momentum-shell renormalization-group flow from simulation.
Our recently developed Fourier Monte Carlo algorithm permits a nonperturbative calculation of momentum-shell renormalization-group flows by simulation which despite its apparent simplicity is illustrative both numerically as well as conceptually interesting. We study the example of a varphi(4) model with long-range lattice interaction. For this model we show that the topology of the renormalization flow is globally accessible in a particularly convenient way. The nontrivial fixed point of Wilson-Fisher type is observed its accompanying critical exponents are numerically determined from fitting its surrounding flow pattern to a linearized renormalization-group transformation. The results are compared to those obtained from perturbation theory, -expansion and earlier Monte Carlo simulations. Application of our method is also expected to be rewarding in other models with long-range interactions.
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Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria. andreas.troester@univie.ac.at