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Lov\'asz and Plummer conjectured, in the mid 1970's, that every cubic graph Gwith no cutedge has an exponential in |V(G)| number of perfect matchings. Inthis work we show that every cubic planar graph G whose geometric dual graph isa stack triangulation has at least 3 times the golden ratio to |V(G)|/72distinct perfect matchings. Our work builds on a novel approach relatingLov\'asz and Plummer's conjecture and the number of so called groundstates ofthe widely studied Ising model from statistical physics.

Counting perfect matchings of cubic graphs in the geometric dual