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Directed Polymers and Interfaces in Disordered Media

We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the model contribute. The structure of field space is analysed for polymers and interfaces at finite temperature using the saddle-point equations derived from each integer moments of the partition function. For the case of an interface we obtain the wandering exponent $ξ= (4-d)/2$, also obtained by the conventional replica method for the replica symmetric scenario.