A Monte Carlo method is used to study $N\times N\times N$ simple-cubic Ising lattices with periodic boundary conditions and free edges. For both types of boundary conditions the position of the specific-heat maximum varies for large $N$ as $a{N}^{-\lambda }$, where $\lambda$ has the scaling value $\lambda ={\nu }^{-1\mathrm{}}$. Both the thermal and magnetic properties are shown to obey finite-size scaling. The free-edge data are shown to be consistent with a surface contribution described by the scaling exponents ${\alpha }_s=\alpha +\nu$, ${\beta }_s=\beta -\nu$, ${\gamma }_s=\gamma +\nu$. Using the free-edge data we also consider corrections to scaling in the infinite lattice and discuss "rounding" in real systems in terms of surface contributions from grains.

• Received 22 January 1976

DOI:https://doi.org/10.1103/PhysRevB.14.255