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We discuss finite-size effects in one disordered ${\lambda}{\phi}^{4}$ modeldefined in a $d$-dimensional Euclidean space. We consider that the scalar fieldsatisfies periodic boundary conditions in one dimension and it is coupled witha quenched random field. In order to obtain the average value of the freeenergy of the system we use the replica method. We first discuss finite-sizeeffects in the one-loop approximation in $d=3$ and $d=4$. We show that in bothcases there is a critical length where the system develop a second-order phasetransition, when the system presents long-range correlations with power-lawdecay. Next, we improve the above result studying the gap equation for thesize- dependent squared mass, using the composite field operator method. Weobtain again, that the system present a second order phase transition withlong-range correlation with power-law decay.

Finite-Size Effects in Disordered $\lambda\phi^{4}$ Model