  The renormalized entanglement entropy (REE) across a circle of radius R has
been proposed as a c-function in Poincar\'e invariant (2+1)-dimensional field
theory. A proof has been presented of its monotonic behavior as a function of
R, based on the strong subadditivity of entanglement entropy. However, this
proof does not directly establish stationarity of REE at conformal fixed points
of the renormalization group. In this note we study the REE for the free
massive scalar field theory near the UV fixed point described by a massless
scalar. Our numerical calculation indicates that the REE is not stationary at
the UV fixed point.
