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The 2D quantum phase transition that occurs in a square lattice of $p+ip$superconductors is used to show how four-body interactions in $d=2$ reproducenonperturbative effects familiar from the study of two-body interactions in$d=1$. This model can be analyzed using an exact lattice self-duality of theassociated 3D classical model; this duality is the 3D generalization of theKramers-Wannier duality of the 2D Ising model, and there are similar exactdualities for certain many-spin interactions in dimensions $d \geq 3$. We alsodiscuss the excitation spectrum in the ordered and disordered phases, and therelationship between our model and previously studied metallic behavior ofboson models with four-boson interactions.Comment: 4 page

physical review letters

Strong-Weak Coupling Self-Duality in the Two-Dimensional Quantum Phase Transition of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:mi>p</mml:mi></mml:math>Superconducting Arrays

Strong-Weak Coupling Self-Duality in the Two-Dimensional Quantum Phase Transition ofp+ipSuperconducting Arrays