  We study thermal phase transitions of color superconductivity by the lattice
simulations of the Ginzburg-Landau (GL) effective theory. The theory is
equivalent to the SU_ f(3) cross SU_c(3) Higgs model coupled to SU_c(3) color
gauge fields. From the eigenvalues of a 3-by-3 gauge-invariant diquark
composite, a clear distinction between the 2-flavor color superconductivity
(2SC) and the color flavor locking (CFL) phase is made in a gauge invariant
manner. The thermal transitions between the normal phase and the
superconducting phases are found to be first-order due to thermal gluons. The
phase structure in the coupling-constant space is numerically explored and
three patterns of phase transition, i.e., normal to 2SC, normal to CFL and
normal to CFL via 2SC, are found in the chiral limit. These results agree
qualitatively with the weak-coupling analysis of the GL theory.
