Noise-induced phase transition in soft Ising spins with a fluctuating interaction

We investigate noise-induced phase transitions in soft Ising spins, which have continuous values, with a fluctuating interaction within the framework of the mean-field scheme. The fluctuating interaction provides an effective ferromagnetic coupling, leading to a ferromagnetic order. The interplay of the fluctuating interaction and an additive noise leads to a reentrant transition, triple transitions, and a softening of the order parameter, presenting a weak order in the ordered phase. In the limit of Ising spins the fluctuating interaction renormalizes the mean field, reducing the critical intensity of the additive noise.