Renormalization group and effective potential: a simple non-perturbative approach

We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of converting the exact renormalization group into a self-consistent renormalization method. It yields a simple second order differential equation for the effective potential. The equation can be solved and its solution is compared with other non-perturbative results and with results of perturbation theory. In three dimensions, we are led to study the sextic field theory (

\lambda\phi^4+g\phi^6

). We work out this theory at two-loop perturbative order and find the non-perturbative approach to be superior.

Note:

36 pages, 1 figure; mass renormalization, comments, espec. on symmetry breaking, references added

dimension: 3
renormalization group: fixed point
nonperturbative
effective potential
perturbation theory
differential equations
critical phenomena
renormalization

References(51)

Figures(1)

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