The light mesons such as pi, rho, omega, f0, and a0 are possible
candidates of magnetic degrees of freedom, if a magnetic dual
picture of QCD exists. We construct a linear sigma model to
describe spontaneous breaking of the magnetic gauge group, in
which there is a stable vortex configuration of vector and scalar
mesons. We numerically examine whether such a string can be
interpreted as the confining string. By using meson masses and
couplings as inputs, we calculate the tension of the string as well as
the strength of the Coulomb force between static quarks. They are
found to be consistent with those inferred from the quarkonium
spectrum and the Regge trajectories of hadrons. By using the same
Lagrangian, the critical temperature of the QCD phase transition is
estimated, and a non-trivial flavor dependence is predicted. We also
discuss a possible connection between the Seiberg duality and the
magnetic model we studied.