Directed paths in random media

 6 vertex model maps to configurations of non-crossing directed paths, possibly navigating a random energy landscape

 For 1 DPRM the partition function is computed by summing over all directed paths, as

 For ease of computation the random energies on the (green) bonds of the vertex model are selected as:

             

 The Transfer Matrices for 1 DPRM now takes the simple form:

For each t-slice L random energies are taken uniformly from a finite interval.

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