  It is pointed out that one-component \phi^4 lattice theory in four dimensions
has a non-perturbative sector which can be studied by means of an exact duality
transformation of its Ising limit. This duality maps it to a membrane model. As
a consequence, the \phi^4-theory turns out to have, in the broken symmetry
phase, a remarkably rich spectrum of physical states corresponding to membrane
excitations. A numerical study of the correlators between dual variables allows
to evaluate the masses of the first few states.
