  We numerically obtain the conformal spectrum of several classical spin models
on a two-dimensional lattice with open boundaries, for every boundary fixed
point obtained by the Cardy's derivation [J. L. Cardy, Nucl. Phys. B 324, 581
(1989)]. In order to extract accurate conformal data, we implement the tensor
network renormalization algorithm [G. Evenbly and G. Vidal, Phys. Rev. Lett.
115, 180405 (2015)] extended so as to be applicable to a square lattice with
open boundaries. We successfully compute the boundary conformal spectrum
consistent with the underlying boundary conformal field theories (BCFTs) for
the Ising, tri-critical Ising, and 3-state Potts models on the lattice, which
allows us to confirm the validity of the BCFT analyses for the surface critical
behaviors of those lattice models.
