Abstract
We consider the problem of directed polymers in a random medium of a finitedimensional lattice. In the high-temperature phase of this system it is known that the annealed and quenched free energies coincide. Upper bounds on the transition temperature to a low-temperature phase had previously been obtained by calculating the first two moments 〈Z〉 and 〈Z2〉 of the partition function. We improve these bounds by estimating noninteger moments 〈Zα〉 for 1<α<2.
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Evans, M.R., Derrida, B. Improved bounds for the transition temperature of directed polymers in a finite-dimensional random medium. J Stat Phys 69, 427–437 (1992). https://doi.org/10.1007/BF01053800
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DOI: https://doi.org/10.1007/BF01053800