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We present an exactly solvable model of a Gaussian (flexible) polymer chainin a quenched random medium. This is the case when the random medium obeys verylong range quadratic correlations. The model is solved in $d$ spatialdimensions using the replica method, and practically all the physicalproperties of the chain can be found. In particular the difference between thebehavior of a chain that is free to move and a chain with one end fixed iselucidated. The interesting finding is that a chain that is free to move in aquadratically correlated random potential behaves like a free chain with $R^2\sim L$, where $R$ is the end to end distance and $L$ is the length of thechain, whereas for a chain anchored at one end $R^2 \sim L^4$. The exactresults are found to agree with an alternative numerical solution in $d=1$dimensions. The crossover from long ranged to short ranged correlations of thedisorder is also explored.Comment: REVTeX, 28 pages, 12 figures in eps forma

A solvable model of a polymer in random media with long-range disorder correlations