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We develop a fermionic formulation of the triangular lattice Isingantiferromagnet (TIAFM) which is both calculationally convenient andintuitively appealing to imaginations steeped in conventional condensed matterphysics. It is used to elucidate a variety of aspects of zero-temperaturemodels. Cylindrical systems possess multiple "phases" distinguished by thenumber of circumferential satisfied bonds and by entropy density. On the plane,phases are labelled by densities of satisfied bonds of two differentorientations. A local particle (semi)conservation law in the fermionic picturelies behind both these features as well as the classic power-law falloff of thespin-spin correlation function, which is also derived from the fermionicperspective.

Triangular Ising antiferromagnet through a fermionic lens, part 1: free energy, zero-temperature phases and spin-spin correlation