  In low-dimensional magnets, thermal agitation and spatial disorders generate
strong spin fluctuations that suppress the long-range magnetic ordering. We
develop an analytical equation for the equilibrium magnetization of
two-dimensional magnets at finite temperatures in the presence of the random
magnetic field. We find that the random field induces a first-order phase
transition in addition to the reduced Curie temperature. The first-order phase
transition persists even in the presence of the moderate external magnetic
field.

Mesoscale and Nanoscale Physics