We introduce a class of exactly solvable models exhibiting an ordering nois
e-induced phase transition in which order arises as a result of a balance b
etween the relaxing deterministic dynamics and the randomizing character of
the fluctuations. A finite-size scaling analysis of the phase transition r
eveals that it belongs to the universality class of the equilibrium Ising m
odel. All these results are analyzed in the light of the nonequilibrium pro
bability distribution of the system, which can be obtained analytically. Ou
r results could constitute a possible scenario of inverted phase diagrams i
n the so-called lower critical solution temperature transitions.