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.