  The site reduction of U(1) lattice gauge theory is used to model the 0-branes
in the dual theory. The reduced theory is the 1D plane-rotator model of the
angle-valued coordinates on discrete world-line. The energy spectrum is
obtained exactly via the transfer-matrix method, with a minimum in the lowest
energy as a direct consequence of compact nature of coordinates. Below the
critical coupling $g_c=1.125$ and temperature $T_c=0.335$ the system undergoes
a first order phase transition between coexistent phases with lower and higher
gauge couplings. The possible relation between the model and the proposed role
for magnetic monopoles in confinement mechanism based on dual Meissner effect
is pointed.
