  For the first time the persistent current in a 2D free-electron system has
been calculated analytically. The tight binding model is considered on a square
lattice with filling factor 1/2. The array has a shape of rectangle with
boundary conditions in both directions twisted by $2\pi\phi_x$ and
$2\pi\phi_y$. The components of the twist are associated with two components of
the magnetic flux in torus geometry. An analytical expression is obtained for
the energy and for the components of the persistent current (PC) at a given
flux and temperature. It is shown that at zero temperature the PC density is
proportional to the vector potential with the coefficient which does not depend
on the size of the system. This happens because the Fermi surface for a square
lattice at filling factor 1/2 is flat. Both the energy and the PC are periodic
functions of the two flux components with the periods $\phi_0/q$ and $\phi_0/s$
where $\phi_0=hc/e$, and $q$ and $s$ are integers which depend on the aspect
ratio of the rectangle. The magnitude of PC is the same as in superconductors.
Therefore, a 3D system constructed from a macroscopic number of isolated
coaxial cylinders at zero temperature reminds the London's superconductor. It
exhibits the quantization of trapped flux as well as the Meissner effect.
However, all the phenomena are of a mesoscopic nature. The critical field $H_c$
decays with an effective size of the system, $H_c\sim 1/R_{ef}$. The magnitude
of PC decays with $T$ as $\exp(-\pi TR_{ef}/2at)$, where $t$ is the hopping
amplitude and $a$ is the lattice constant.
