Boundary conditions and variable ground state entropy for the antiferromagnetic Ising model on a triangular lattice.

The ground state entropy density of the antiferromagnetic Ising model on a triangular lattice is considered in the infinite volume limit as a function of boundary conditions on a finite triangular domain. The ground states of this domain do not map to a dimer covering and so cannot be classified into string sectors. A parametrized boundary condition is identified that allows the entropy density to be tuned to values between nondegeneracy and maximal degeneracy. The results are compared to those for a rectangular periodic domain for which the ground states can be classified into string sectors.

Recovery of limited-extent images aliased because of spectral undersampling.

In imaging situations where observations are made in spatial-frequency space, it is often desirable to lower the number of observations to fewer than that imposed by the Nyquist criterion. It is shown that patterns of regular spectral undersampling lead to aliasing that can be partially eliminated from some regions of a limited-extent image. An algorithm is presented for determining which regions are recoverable and which are not for a given pattern. Noniterative recovery, analogous to that proposed by Walsh and Nielsen-Delaney [J. Opt. Soc. Am. A 11, 572 (1994)], is shown to be feasible in cases of regular undersampling. The work has particular relevance to magnetic resonance imaging and aperture synthesis telescopy.