The axial magnetic phase diagram of the antiferromagnet Fe0.95Mg0.05Br2 is studied by specific heat, superconducting quantum interference device, and Faraday rotation techniques. The diamagnetic impurities give rise to random-field criticality along the second-order phase line Hc(T) between TN=13.1 K and a multicritical point at Tm≈5 K, and to a spin-flop line between Tm and the critical end-point temperature Te≈3.5 K. The phase line H1(T)c(T) ending at Tm is probably due to symmetric nondiagonal exchange