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We study cutoff and lattice effects in the O(n) symmetric $\phi^4$ theory fora $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions.In the large-N limit above $T_c$, we show that $\phi^4$ field theory at finitecutoff $\Lambda$ predicts the nonuniversal deviation $\sim (\Lambda L)^{-2}$from asymptotic bulk critical behavior that violates finite-size scaling anddisagrees with the deviation $\sim e^{-cL}$ that we find in the $\phi^4$lattice model. The exponential size dependence requires a non-perturbativetreatment of the $\phi^4$ model. Our arguments indicate that these resultsshould be valid for general $n$ and $d > 2$.

Cutoff and lattice effects in the theory of confined systems