Phase Diagram of a Superconducting and Antiferromagnetic System with SO(5) Symmetry

Temperature vs chemical-potential phase diagrams of an SO(5) model for high- $T_c$ cuprates are calculated by Monte Carlo simulation. There is a bicritical point where the second-order antiferromagnetism (AF) and superconductivity transition lines merge tangentially into a first-order line, and the SO(5) symmetry is achieved. In an external magnetic field, the AF ordering is first order in the region near the cross point of the AF transition line and the first-order melting line of flux lattice; there is a tricritical point on the AF transition line from which the AF ordering becomes second order.