Satisfying states of triangulations of a convex n-gon

In this work we count the number of satisfying states of triangulations of a convex n-gon using the transfer matrix method. We show an exponential (in n) lower bound. We also give the exact formula for the number of satisfying states of a strip of triangles.Comment: 17 pages, 6 figure

Non-degenerated groundstates in the antiferromagnetic Ising model on triangulations

A triangulation is an embedding of a graph into a closed Riemann surface so that each face boundary is a 3-cycle of the graph. In this work, groundstate degeneracy in the antiferromagnetic Ising model on triangulations is studied. We show that for every fixed closed Riemann surface S, there are vertex-increasing sequences of triangulations of S with a non-degenerated groundstate. In particular, we exhibit geometrically frustrated systems with a non-degenerated groundstate.Comment: 11 pages, 9 figure