  I study the universal finite-size scaling function for the lowest gap of the
quantum Ising chain with a one-parameter family of ``defect'' boundary
conditions, which includes periodic, open, and antiperiodic boundary conditions
as special cases. The universal behavior can be described by the Majorana
fermion field theory in $1+1$ dimensions, with the mass proportional to the
deviation from the critical point. Although the field theory appears to be
symmetric with respect to the inversion of the mass (Kramers-Wannier duality),
the actual gap is asymmetric, reflecting the spontaneous symmetry breaking in
the ordered phase which leads to the two-fold ground-state degeneracy in the
thermodynamic limit. The asymptotic ground-state degeneracy in the ordered
phase is realized by (i) formation of a bound state at the defect (except for
the periodic/antiperiodic boundary condition) and (ii) effective reversal of
the fermion number parity in one of the sectors (except for the open boundary
condition), resulting in a rather nontrivial crossover ``phase'' diagram in the
space of the boundary condition (defect strength) and mass.
