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Related Experiment Videos

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps.

S Caracciolo1, M S Causo, A Pelissetto

  • 1Scuola Normale Superiore, INFN and INFM, I-56100 Pisa, Italy. Sergio.Caracciolo@sns.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
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This study explores crossover phenomena in self-avoiding walks, bridging Gaussian and Wilson-Fisher fixed points. Numerical simulations and field theory confirm predictions for critical crossover functions and scaling behavior.

Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Self-avoiding walks (SAWs) are fundamental models in statistical physics.
  • Medium-range interactions introduce complex crossover phenomena.
  • Understanding transitions between different universality classes is crucial.

Purpose of the Study:

  • To investigate critical crossover phenomena in a SAW model with medium-range jumps.
  • To analyze the interpolation between Gaussian and Wilson-Fisher fixed points.
  • To validate theoretical predictions with numerical simulations.

Main Methods:

  • Field-theoretical methods were employed to compute crossover functions.
  • An appropriate mean-field expansion was utilized.

Related Experiment Videos

  • Numerical Monte Carlo simulations were performed for walk models.

    • Main Results:

    • Good agreement was found between Monte Carlo data and field-theoretical predictions.
    • The scaling behavior of leading nonuniversal corrections was verified.
    • Phenomenological parametrizations accurately described nonuniversal crossover behavior.

    Conclusions:

    • The study successfully characterized critical crossover phenomena in the studied SAW model.
    • Field-theoretical predictions are well-supported by efficient numerical simulations.
    • Developed parametrizations offer a comprehensive description of crossover behavior.