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