  Using a specially designed Monte Carlo algorithm with directed loops, we
investigate the triangular lattice Ising antiferromagnet with coupling beyond
nearest neighbour. We show that the first-order transition from the stripe
state to the paramagnet can be split, giving rise to an intermediate nematic
phase in which algebraic correlations coexist with a broken symmetry.
Furthermore, we demonstrate the emergence of several properties of a more
topological nature such as fractional edge excitations in the stripe state, the
proliferation of double domain walls in the nematic phase, and the Kasteleyn
transition between them. Experimental implications are briefly discussed.
