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Consider the partition function of a directed polymer in an IID field. Weassume that both tails of the negative and the positive part of the field areat least as light as exponential. It is a well-known fact that the free energyof the polymer is equal to a deterministic constant for almost everyrealization of the field and that the upper tail of the large deviations isexponential. The lower tail of the large deviations is typically lighter thanexponential. In this paper we provide a method to obtain estimates on the rateof decay of the lower tail of the large deviations, which are sharp up tomultiplicative constants. As a consequence, we show that the lower tail of thelarge deviations exhibits three regimes, determined according to the tail ofthe negative part of the field. Our method is simple to apply and can be usedto cover other oriented and non-oriented models including first/last-passagepercolation and the parabolic Anderson model

Large Deviations for Partition Functions of Directed Polymers and Some Other Models in an IID Field