Abstract
Directed polymers in a random media draw much attention because of its relevance to many physical phenomena. In this paper, utilizing the precise numerical procedure proposed in our previous work for directed polymers in 1+1 and 2+1 dimensions, we present systematic numerical simulations for directed polymers in 3+1 dimensions at finite temperatures. Our numerical simulations suggest a phase transition in the transverse fluctuations, the free energy fluctuations, the entropy fluctuations and the internal energy fluctuations for directed polymers in 3+1 dimensions. It is found out that the entropy fluctuations reach a maximum around the critical temperature. There is no phase transition for the ensemble energy fluctuations. As a consequence of the specific heat scales as t, the ensemble energy fluctuations scales as t1/2 at any finite temperature.
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