Monopoles, confinement and deconfinement in lattice compact QED in (2+1)D with external fields

Finite temperature compact electrodynamics in (2+1) dimensions is studied in the presence of external electromagnetic fields. The deconfinement temperature is found to be insensitive to the external fields. This result corroborates our observation that external fields create additional small--size magnetic dipoles from the vacuum which do not spoil the confining properties of the model at low temperature. However, the Polyakov loop is not an order parameter of confinement. It can vanish in deconfinement in the presence of external field. This does not mean the restoration of confinement for certain external field fluxes. As a next step in the study of (2+1)D QED, the influence of monopoles on the photon propagator is studied. First results are presented showing this connection in the confining phase (without external field)