  The one-component $\lambda\phi^4$ theory in four dimensions in the
spontaneously broken symmetry phase has a non-trivial, non-perturbative sector
which can be studied by means of a duality transformation of its Ising limit.
Duality maps this theory to a model of interacting membranes. Physical states
correspond to membrane excitations. The way this non-perturbative behaviour can
be reconciled with the triviality of the theory in its continuum limit is
discussed.
