Three-dimensional massive scalar field theory and the derivative expansion of the renormalization group |
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| Affiliation: | 1. Department of Physics, Sophia University, Tokyo 102-8554, Japan;2. Department of Physics, the University of Tokyo 113-0033, Japan;1. Faculty of Physics, Baku State University, AZ-1148, Baku, Azerbaijan;2. Physics Department, Middle East Technical University, 06531 Ankara, Turkey;1. Physics Department and Center for Exploration of Energy and Matter, Indiana University, 2401 N Milo B. Sampson Lane, Bloomington, IN 47408, USA;2. Institute of Particle Physics and Key Laboratory of Quark & Lepton Physics (MOE), Central China Normal University, Wuhan, 430079, China;1. Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, Jiangsu 210023, PR China;2. School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, PR China;3. Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing, Jiangsu 210023, PR China |
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| Abstract: | We show that non-perturbative fixed points of the exact renormalization group, their perturbations and corresponding massive field theories can all be determined directly in the continuum — without using bare actions or any tuning procedure. As an example, we estimate the universal couplings of the non-perturbative three-dimensional one-component massive scalar field theory in the Ising model universality class, by using a derivative expansion (and no other approximation). These are compared to the recent results from other methods. At order derivative-squared approximation, the four-point coupling at zero momentum is better determined by other methods, but factoring this out appropriately, all our other results are in very close agreement with the most powerful of these methods. In addition we provide for the first time, estimates of the n-point couplings at zero momentum, with n = 12, 14, and the order momentum-squared parts with n = 2,…, 10. |
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