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Critical behavior and scaling in trapped systems.

Massimo Campostrini1, Ettore Vicari

  • 1Dipartimento di Fisica dell'Università di Pisa and INFN, I-56127 Pisa, Italy.

Physical Review Letters
|August 8, 2009
PubMed
Summary

We found a new scaling behavior, trap-size scaling, for critical particle systems in potentials. This scaling, characterized by the critical exponent theta, describes how correlation length depends on trap size near the critical temperature.

Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Critical Phenomena

Background:

  • Particle systems near critical points exhibit universal behaviors.
  • Confinement by potentials can alter these critical properties.
  • Finite-size scaling theory describes systems near boundaries.

Purpose of the Study:

  • To investigate the scaling properties of critical particle systems confined by potentials.
  • To introduce and analyze the concept of trap-size scaling.
  • To determine the critical exponent governing this scaling behavior.

Main Methods:

  • Renormalization-group (RG) arguments were employed to derive scaling relations.
  • Numerical simulations were performed on two-dimensional lattice gas (Ising) models.

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  • Various harmonic traps were used to study the effect of confinement.

    • Main Results:

    • A novel trap-size scaling behavior was identified for confined critical systems.
    • A nontrivial trap critical exponent (theta) was defined, relating correlation length (xi) to trap size (l) as xi ~ l^theta.
    • The exponent theta was shown to depend on the universality class, potential type, and coupling to critical modes.

    Conclusions:

    • Trap-size scaling provides a new framework for understanding confined critical phenomena.
    • Numerical results for 2D lattice gas models support the proposed scaling scenario.
    • The study reveals how confinement modifies the critical behavior of particle systems.