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Exact calculation of the anomalous dimension of the diffusion coefficient for a model of a random walk in a random potential. (English) Zbl 0707.60104

Summary: Renormalisation of a model of classical diffusion in a random potential is analysed. It is shown that at two dimensions the one-loop expression for the anomalous dimension of the diffusion coefficient is perturbatively exact leading to the coupling-dependent value \(1/\nu =2+g/4\pi\) of the exponent \(\nu\).

MSC:

60K40 Other physical applications of random processes
82B26 Phase transitions (general) in equilibrium statistical mechanics
60G50 Sums of independent random variables; random walks
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