  K$_2$CuF$_4$ is magnetically described as a spin-1/2, quasi-two-dimensional
(2D), square-lattice XXZ ferromagnet with weak easy-plane anisotropy. The
magnetic ordering for an applied magnetic field $H$ parallel to the $c$ axis is
equivalent to the Bose\,--\,Einstein condensation (BEC) of lattice bosons, as
discussed by Matsubara and Matsuda [Prog. Theor. Phys. \textbf{16}, 569
(1956)]. Magnetization and specific heat measurements were performed to obtain
the temperature vs magnetic field phase diagram for $H\,{\parallel}\,c$. The
phase boundary between polarized and ordered phases was found to be expressed
by the power law $H_{\rm c}(T)\,{-}\,H_{\rm c}(0)\,{\propto}\,T^\phi$ with
exponent $\phi\,{\approx}\,1.0$ in a wide temperature range, in agreement with
the theory of quasi-2D BEC.
