Based on the results published recently [SciPost Phys. 7, 026
(2019)], the influence of surfaces and boundary fields are calculated
for the ferromagnetic anisotropic square lattice Ising model on finite
lattices as well as in the finite-size scaling limit. Starting with the
open cylinder, we independently apply boundary fields on both sides
which can be either homogeneous or staggered, representing different
combinations of boundary conditions. We confirm several predictions from
scaling theory, conformal field theory and renormalisation group theory:
we explicitly show that anisotropic couplings enter the scaling
functions through a generalised aspect ratio, and demonstrate that open
and staggered boundary conditions are asymptotically equal in the
scaling regime. Furthermore, we examine the emergence of the surface
tension due to one antiperiodic boundary in the system in the presence
of symmetry breaking boundary fields, again for finite systems as well
as in the scaling limit. Finally, we extend our results to the
antiferromagnetic Ising model.
Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields
