Random Ginzburg-Landau model revisited: reentrant phase transitions

We analyze the phase diagram of the random Ginzburg-Landau model, where a quenched dichotomous noise affects the control parameter. We show that the system exhibits two types of counterintuitive reentrant second-order phase transitions. In the first case, increasing the coupling drives the system from a disordered to an ordered state and then back to a disordered state. In the second case, increasing the intensity of the quenched noise, the system goes from an ordered phase to a disordered phase and back to an ordered state. We discuss the general mechanism that produces these reentrant phase transitions, showing that it may appear in other physical systems, such as a modification of the spin-1 Blume-Capel model proposed to describe the critical behavior of helium mixtures in a random medium.