  The antiferromagnetic Ising model is investigated on the 20 2-uniform
lattices using the Monte-Carlo method based on the Wang-Landau algorithm and
the Metropolis algorithm to study the geometric frustration effect
systematically. Based on the specific heat, the residual entropy, and the
Edwards-Anderson freezing order parameter, the ground states of them were
determined. In addition to the long-range-ordered phase and the spin ice phase
found in the Archimedean lattices, two more phases were found. The partial
long-range order is long-range order with exceptional disordered sites, which
gives extensive residual entropy. In the partial spin ice phase, the partial
freezing phenomenon appears: Majority of sites are frozen without long-range
order, but the other sites are fluctuating even at zero temperature. The spin
liquid ground state was not found in the 2-uniform lattices.

Statistical Mechanics