Entropy fluctuations for directed polymers in [Formula Presented] dimensions

Xiao Hong Wang, Shlomo Havlin, Moshe Schwartz

Research output: Contribution to journalArticlepeer-review


We find numerically that the sample to sample fluctuation of the entropy (Formula presented) is a more sensitive tool in distinguishing low from high temperature behaviors than the common corresponding fluctuation in the free energy. In (Formula presented) dimensions we find a single phase for all temperatures, since (Formula presented) is always extensive. In (Formula presented) dimensions we find a behavior that at first sight might appear to be a transition from a low temperature phase where (Formula presented) 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 argument to obtain (Formula presented) for high temperature, and find that while it is always extensive it is also extremly small, and that the leading extensive part decays very quickly to zero as the temperature is increased.


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