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The four-dimensional \phi^4 theory is usually considered to be trivial in thecontinuum limit. In fact, two definitions of triviality were mixed in theliterature. The first one, introduced by Wilson, is equivalent to positivenessof the Gell-Mann -- Low function \beta(g) for g\ne 0; it is confirmed by allavailable information and can be considered as firmly established. The seconddefinition, introduced by mathematical community, corresponds to the truetriviality, i.e. principal impossibility to construct continuous theory withfinite interaction at large distances: it needs not only positiveness of\beta(g) but also its sufficiently quick growth at infinity. Indications oftrue triviality are not numerous and allow different interpretation. Accordingto the recent results, such triviality is surely absent.

Is \phi^4 theory trivial ?