Non-degenerated groundstates in the antiferromagnetic Ising model on triangulations

Details Non-degenerated groundstates in the antiferromagnetic Ising model on triangulations Non-degenerated groundstates in the antiferromagnetic Ising model on triangulations

2011-10-11

arxiv.org/abs/1110.2507v1

Mathematics

Combinatorics

11 pages, 9 figures

Scientific paper

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.

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