Classical frustratedXYmodel: Continuity of the ground-state energy as a function of the frustration

The uniformly frustrated classical XY model can describe Josephson-junction arrays in a transverse magnetic field. It has been suggested that the energy E(f) and the T=0 critical current ${\mathit{i}}_{\mathit{c}}$(f) in the ground state may be highly discontinuous functions when the frustration parameter f goes through rational and irrational values. We show here that E(f) is a continuous function for a wide class of spin-spin interacting potentials including the cosine for which E(f) will be strictly negative for all f. We discuss the behavior of ${\mathit{i}}_{\mathit{c}}$(f) and we show that ${\mathit{i}}_{\mathit{c}}$(f) has a strictly positive lower bound in the case of piecewise parabolic interacting potential.