Average Action for the $N$ Component $\phi^4$ Theory

Ringwald, A.; Wetterich, C.

doi:10.1016/0550-3213(90)90489-Z

Average Action for the $N$ Component $\phi^4$ Theory

A. Ringwald
(
- DESY
)
,
C. Wetterich
(
- DESY
)

Jun, 1989

21 pages

Published in:

Nucl.Phys.B 334 (1990) 506-526

Published: 1990

DOI:

10.1016/0550-3213(90)90489-Z

Report number:

DESY-89-068

reference search122 citations

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Abstract: (Elsevier)

The average action is a continuum version of the block spin action in lattice field theories. We compute the one-loop approximation to the average potential for the N -component ϕ 4 theory in the spontaneously broken phase. For a finite (linear) block size ∼ k −1 this potential is real and nonconvex. For small ϕ the average potential is quadratic, U k = − 1 2 k 2 ϕ 2 , and independent of the original mass parameter and quartic coupling constant. It approaches the convex effective potential as k vanishes.

phi**n model: 4
symmetry: O(N)
lattice field theory: action
block spin transformation
spontaneous symmetry breaking
perturbation theory: higher-order
potential
expansion: weak coupling
weak coupling: expansion

References(9)

Figures(0)

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Average Action for the NNN Component ϕ4\phi^4ϕ4 Theory

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Average Action for the $N$ Component $\phi^4$ Theory