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We investigate the chiral phase transition of a QCD-like theory, based theshape change of the effective potential near the critical point. The potentialis constructed with the auxiliary field method, and a source term coupled tothe field is introduced in order to compute the potential shape numerically. Wealso generalize the potential so as to have two independent order parameters,the quark scalar density and the number density. We find a tri-critical pointlocating at (T,mu)=(97, 203) MeV, and visualize it as the merging point ofthree potential minima.Comment: 6 pages 4 figures, to appear in a special issue of Int. J. of Mod.  Phys. E (the proceedings of the 19th International Conference on  Ultrarelativistic Nucleus-Nucleus Collisions: Quark Matter 2006 (QM 2006),  Shanghai, China, 14-20 Nov 2006

LANDAU POTENTIAL STUDY OF THE CHIRAL PHASE TRANSITION IN A QCD-LIKE THEORY