Replicating Higgs fields in Ising gauge theory: the registry order
Abstract
We consider Z2 gauge field theory coupled to "Higgs" matter fields invoking several copies of such matter, interacting entirely through the gauge fields, the Z2 × Z2 × Z2·s / Z2 and the O(N) × O(N) × O(N) ·s / Z2 families of theories. We discover that the Higgs phase of such theories is characterized by a hitherto unidentified "registry" order parameter. This is characterized by a gauge invariant p = 2Nrep/2 Potts type symmetry where Nrep is the number of matter copies. The meaning of this registry is that the different matter copies align their vectors locally in strictly parallel or anti-parallel fashion, even dealing with the continuous O(2) symmetry. Supported by Monte-Carlo simulations, we identify the origin of this registry order in terms of the gauge interactions mediated by the fluxes ("visons") associated with the Z2 gauge fields, indirectly imposing the discrete symmetry in the gauge invariant global symmetry controlled effective order parameter theory. In addition, it appears that our simulations reveal a hitherto unidentified "pseudo-universality" associated with the very similar form of the overall phase diagrams of the various theories suggesting a remarkable "governance" by the gauge field part of the dynamics.