  An asymmetrical 2D Ising model with a zigzag surface, created by diagonally
cutting a regular square lattice, has been developed to investigate the
thermodynamics and phase transitions on surface by the methodology of recursive
lattice, which we have previously applied to study polymers near a surface. The
model retains the advantages of simple formulation and exact calculation of the
conventional Bethe-like lattices. An antiferromagnetic Ising model is solved on
the surface of this lattice to evaluate thermal properties such as free energy,
energy density and entropy, from which we have successfully identified a first
order order-disorder transition other than the spontaneous magnetization, and a
secondary transition on the supercooled state indicated by the Kauzmann
paradox.
