The scaling window of the 5D Ising model with free boundary conditions

The five-dimensional Ising model with free boundary conditions has recently received a renewed interest in a debate concerning the finite-size scaling of the susceptibility near the critical temperature. We provide evidence in favour of the conventional scaling picture, where the susceptibility scales as L2L2 inside a critical scaling window of width 1/L21/L2. Our results are based on Monte Carlo data gathered on system sizes up to L=79L=79 (ca. three billion spins) for a wide range of temperatures near the critical point. We analyse the magnetisation distribution, the susceptibility and also the scaling and distribution of the size of the Fortuin–Kasteleyn cluster containing the origin. The probability of this cluster reaching the boundary determines the correlation length, and its behaviour agrees with the mean field critical exponent δ=3δ=3, that the scaling window has width 1/L21/L2.