Prediction of a first-order phase transition in two-dimensional ferromagnets in the presence of random fields

Random magnetic fields suppress the long-range magnetic ordering through the formation of the magnetic domains. The size of the domains is determined by the competition among the exchange interaction, the magnetic anisotropy , and the strength of the random field. Here we theoretically investigate the temperature dependence of the magnetization of the two-dimensional domains for the anisotropic Heisenberg model with a random magnetic field. We find that magnetization of the domains displays a first-order phase transition in which the magnetization is discontinuous at a critical temperature. Moreover, the first-order transition persists even in the presence of an external magnetic field whose magnitude is smaller than the strength of the disorder. The above unusual first-order phase transition can be experimentally tested with doped two-dimensional magnets.