Entropy fluctuations for directed polymers in 2+1 dimensions

Abstract

We find numerically that the sample to sample fluctuation of the entropy, $\Delta S$, is a tool more sensitive in distinguishing how from high temperature behaviors, than the corresponding fluctuation in the free energy. In 1+1 dimensions we find a single phase for all temperatures since $(\Delta S{)}^2$ is always extensive. In 2+1 dimensions we find a behavior may look at first sight as a transition from a low temperature phase where $(\Delta S{)}^2$ is extensive to a high temperature phase where it is subextensive. This is observed in spite of the relatively large system we use. The observed behavior is explained not as a phase transition but as a strong crossover behavior. We use an analytical agreement to obtain $(\Delta S{)}^2$ for high temperature and find that while it is always extensive it is also extremly small and the leading extensive part decays very fast to zero as temperature is increased.

5 pages, 3 figures, REVTeX, to appear in Phys. Rev. E

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