First-order transition in the l-component spin model with Gaussian random field

Effects of a Gaussian random field on the phase transition of the l-component classical spin vector model are investigated using the replica technique. The phase diagrams are obtained in the cases l=1 and 3. In contrast to what has been predicted by Schneided and Pytte the results we obtained for l=1 and 3 show that the model exhibits a second-order, tricritical point and a first-order transition depending on the value of the random field.