  In order to study the thermodynamic properties of brane-antibrane systems in
the toroidal background, we compute the finite temperature effective potential
of tachyon T in this system on the basis of boundary string field theory. We
first consider the case that all the radii of the target space torus are about
the string scale. If the Dp-antiDp pair is extended in all the non-compact
directions, the sign of the coefficient of |T|^2 term of the potential changes
slightly below the Hagedorn temperature. This means that a phase transition
occurs near the Hagedorn temperature. On the other hand, if the Dp-antiDp pair
is not extended in all the non-compact directions, the coefficient is kept
negative, and thus a phase transition does not occur. Secondly, we consider the
case that some of the radii of the target space torus are much larger than the
string scale and investigate the behavior of the potential for each value of
the radii and the total energy. If the Dp-antiDp pair is extended in all the
non-compact directions, a phase transition occurs for large enough total
energy.
