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Related Experiment Videos

Entropy fluctuations for directed polymers in 2+1 dimensions.

X H Wang1, S Havlin, M Schwartz

  • 1Minerva Center and Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary

Fluctuations in entropy, not free energy, better distinguish temperature behaviors. In 2+1 dimensions, observed behaviors indicate a crossover, not a phase transition, with entropy fluctuations decreasing rapidly at high temperatures.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Computational physics

Background:

  • Distinguishing between low and high temperature phases is crucial in statistical mechanics.
  • Fluctuations in thermodynamic quantities are often used to probe phase transitions and critical phenomena.
  • The fluctuation in free energy is a commonly used, but potentially less sensitive, indicator.

Purpose of the Study:

  • To investigate the sensitivity of entropy fluctuations compared to free energy fluctuations in distinguishing temperature-dependent behaviors.
  • To analyze the dimensional dependence of these fluctuations, specifically in 1+1 and 2+1 dimensions.
  • To clarify the nature of observed phenomena in 2+1 dimensions, determining if they represent phase transitions or crossovers.

Main Methods:

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  • Numerical simulations were employed to calculate entropy fluctuations.
  • Analytical arguments were used to derive high-temperature behavior of entropy fluctuations.
  • The extensivity of the squared entropy fluctuation, (DeltaS)(2), was analyzed in different dimensions.

    • Main Results:

    • Entropy fluctuations (DeltaS) are found to be more sensitive than free energy fluctuations for distinguishing temperature regimes.
    • In 1+1 dimensions, a single phase exists across all temperatures as (DeltaS)(2) remains extensive.
    • In 2+1 dimensions, a crossover behavior is observed, not a phase transition, where (DeltaS)(2) transitions from extensive to subextensive due to its rapid decay at high temperatures.

    Conclusions:

    • Entropy fluctuations provide a more robust tool for characterizing temperature-dependent behaviors in physical systems.
    • The observed phenomena in 2+1 dimensions are attributed to strong crossover effects, with entropy fluctuations becoming negligibly small at high temperatures.
    • The study highlights the importance of considering entropy fluctuations for a deeper understanding of phase behavior and critical phenomena.