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

Abstract:

Monte-Carlo results for the moments of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L () 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 Chen 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 single scaling variable tL ^d/2 where is the temperature distance from the critical temperature, only to a very limited extent. While the CD theory gives a somewhat improved description of corrections to the “lowest-mode” results (to which the CD theory can easily be reduced in the limit , , tL ^d/2 fixed) for the fourth-order cumulant, discrepancies are found for the susceptibility (). Reasons for these problems are briefly discussed.