Setup of Frustration in Potts Spin Systems

Abstract

Frustration in the Potts spin systems is proposed as an extension of the ordinary frustration in the Ising spin systems. We construct a variety of fully-frustrated p -state Potts models on the square lattice by applying the extended frustration inspired by the primitive form on a multi-decorated lattice; the universality class of those fully-frustrated p -state Potts models is the same as that of the ferromagnetic one-state Potts model, which is equivalent to the ordinary percolation system. It is shown that a typical case of the fully-frustrated p -state Potts models can be regarded as the p -mer packing problem at the macroscopically degenerated ground state.