We analyze finite-size effects in a $L^d$ geometry above the upper critical dimension $d=4\mathrm{}$ within the $O\left(n\right)\mathrm{}$ symmetric ${\phi }^4$ theory on the basis of exact results for $\overrightarrow{n}\infty$ and one-loop results for $n=1.\mathrm{}$ We show that finite-size effects of the ${\phi }^4$ continuum theory with a smooth (rather than sharp) cutoff belong to the same universality class as those of the ${\phi }^4$ lattice theory. Our analysis predicts both universal and nonuniversal features of finite-size effects and resolves long-standing discrepancies in earlier analyses of Monte Carlo (MC) data for the $d=5\mathrm{}$ Ising model. Our estimates of two fundamental length scales ${\xi }_0$ and $l_0$ are confirmed by very recent MC data.

• Received 20 April 2000

DOI:https://doi.org/10.1103/PhysRevE.63.016113