Scalar φ^4 theory's symmetric and broken phases are related by a sign flip of the quartic coupling via analytically tractable saddle point expansions.
Romatschke, What ifϕ4 theory in 4 dimensions is non-trivial in the continuum?, Phys
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On self-dualities for scalar $\phi^4$ theory
Scalar φ^4 theory's symmetric and broken phases are related by a sign flip of the quartic coupling via analytically tractable saddle point expansions.