Finite-size scaling above the upper critical dimension revisited: the caseof the five-dimensional Ising model

Monte-Carlo results for the moments [M-k] of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a L-d geometry, where L (4 le ss than or equal to L less than or equal to 22) is the linear dimension of a hypercubic lattice with periodic boundary conditions in d = 5 dimensions, are analyzed in the critical region and compared to a recent theory of Che n and Dohm (CD) [X.S. Chen and V. Dohm, Int. J. Mod. Phys. C 9, 1007 (1998) ]. We show that this finite-size scaling theory (formulated in terms of two scaling variables) can account for the longstanding discrepancies between Monte-Carlo results and the so-called "lowest-mode" theory, which uses a si ngle scaling variable tL(d/2) where t = T/T-c -- 1 is the temperature dista nce from the critical temperature, only to a very limited extent. While the C:D theory gives a somewhat improved description of corrections to the "lo west-mode" results (to which the CD theory can easily be reduced in the lim it t --> 0, L --> infinity, tL(d/2) fixed) for the fourth-order cumulant, d iscrepancies are found for the susceptibility (L-d(M-2)). Reasons for these problems are briefly discussed.