Summary: Phase models for affine linear logic were independently devised by \textit{Y. Lafont} [J. Symb. Log. 62, No. 4, 1202-1208 (1997; Zbl 0897.03010)] and \textit{M. Piazza} [``Phase semantics for linear affine logic'', typescript], although foreshadowed by \textit{H. Ono} [``Semantics for substructural logics'', in: P. Schroeder-Heister et al. (eds.), Substructural logics (Clarendon Press, Oxford), 259-291 (1994; Zbl 0811.68056)]. However, the existing semantics either contain no explicit directions for the construction of models in the general case, or else are forced to resort to additional conditions extending Girard's semantics (preordering of the monoids, the condition that the set of antiphases be an ideal). We dispense with these extra postulates -- at least for the subexponential fragment of this logic -- considering structures where the set of antiphases is concretely constructed. Moreover, we show the equivalence of our phase models and the algebraic models of affine linear logic by means of a representation theorem.