A FINITE-SIZE-SCALING STUDY OF THE 5-DIMENSIONAL ISING-MODEL

For systems above the marginal dimension d*, where mean field theory starts to become valid, such as Ising models in d = 5 for which d* = 4, hyperscaling is invalid and hence it was suggested that finite size scaling is not ruled by the correlation length xi(proportional to\t\(-1/2) in Landau theory, t being the distance from the critical point) but by a ''thermodynamic length'' l(proportional to\t\(-2/d)). Early simulation work by Binder et al. using nearest neighbor hypercubic L(5) lattices with L less than or equal to 7 yielded some evidence for this prediction, but the renormalized coupling constant g(L) = -3+[M(4)]/[M(2)](2) at T-c was g(L) approximate to -1.0 instead of the prediction of Brezin and Zinn-Justin, g(L)(T-c) = -3+Gamma(4)(1/4)/(8 pi(2)) approximate to -0.812. In the present work, we try to shed light on this controversy obtaining much more precise Monte Carlo data using multihistogram techniques and lattices as large as L = 17 (i.e., 1419857 Ising spins). While our value of T-c agrees nicely with recent high temperature series work (k(B)T(c)/J approximate to 8.7774 +/- 0.0035), the coupling at T-c{g(L)(T-c) approximate to -0.958 +/- 0.050} confirms the work for small lattices and disagrees with the analytical prediction. Hence the data are better consistent with a shift of the effective critical temperature T-c(L)-T-c(infinity)proportional to L(-d/2) rather than with L(-(d-2)) according to the analytical theory. If the latter behavior is correct, it can hence be seen for extremely large systems only.