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Three dimensional massive scalar field theory and the derivative expansion of the renormalization group

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arxiv hep-th/9612117 v3 pith:R5EAKGOY submitted 1996-12-11 hep-th cond-mathep-lathep-ph

Three dimensional massive scalar field theory and the derivative expansion of the renormalization group

classification hep-th cond-mathep-lathep-ph
keywords otherfieldmassivemethodsapproximationcouplingsderivativedetermined
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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  1. Asymptotic behaviour of the derivative expansion in the ERG

    hep-th 2026-07 conditional novelty 7.0

    The derivative expansion of the exact renormalization group is divergent for generic operators in any dimension, but behaves as an asymptotic series that converges to high order in common applications.