PHASE STRUCTURE OF DISCRETE ABELIAN SPIN AND GAUGE SYSTEMS

It is shown that in a two-dimensional Zp spin system for p not too small there exists a massless phase in the middle between the ordered and disordered Ising-type phases. A similar thing happens in a four-dimensional Zp gauge theory, where a massless QED-like phase appears between the screened and the confined phases. The existence of the middle phase is deduced logically from the existence of such a phase in the continuous O(2)-invariant models using self-duality and correlation inequalities. For the spin case the transition towards this phase is analyzed using a Kosterlitz type of renormalization group suggesting an essential singularity of the correlation length at both transition points. A Hamiltonian strong-coupling expansion up to ninth order is applied to the Zp spin system. The results of the Padé analysis of this expansion are consistent with the phase structure described above. For p≤4 the analysis suggests two phases with a conventional singularity behavior at the transition. In the nontrivial case of p=3, critical exponents are calculated and found to give good agreement with experiment. For p5 the analysis favors three phases with an essential singularity at the transition. © 1979 The American Physical Society.