Abstract
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 , also obtained by the conventional replica method for the replica symmetric scenario.
Highlights
The statistical mechanics of random surfaces and membranes, or more generally of extended objects, has been widely discussed in the literature, see, e.g., [1]
One is mainly interested in averaging the free energy over the disorder, which amounts to averaging the logarithm of the partition function
We are mainly interested in averaging the free energy over the disorder, which amounts to averaging the logarithm of the partition function
Summary
The statistical mechanics of random surfaces and membranes, or more generally of extended objects, has been widely discussed in the literature, see, e.g., [1]. In the field theory of random manifolds, a technique that has been used in order to compute the average free energy is the replica method [16,17,18,19,20,21]. Let Z k be the k-th power of the partition function, for k integer In this case, we have a perturbative expansion of the average free energy given by Equation (9). Studying the replica field theory for the problem of fluctuating manifold in a quenched random potential, Mézard and Parisi and others introduced a mass term in the effective Hamiltonian in order to regularize the model [30,51]. In the high-temperature limit, ( β → 0), all the moments of the partition functions contribute to the average free energy. Gaussian model defined in the continuous limit and calculate its wandering exponent
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