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

Abstract

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.