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Generalized crossover in multiparameter Hamiltonians.

P Parruccini1, P Rossi

  • 1Dipartimento di Fisica dell'Università di Pisa and INFN-Sezione di Pisa Via Buonarroti, 2-56127 Pisa, Italy. parrucci@df.unipi.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
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Researchers present a new method to characterize crossover lines and surfaces in systems near criticality. This approach links generalized crossover to the vanishing renormalization group function, offering insights into complex physical systems.

Area of Science:

  • * Condensed Matter Physics
  • * Statistical Mechanics

Background:

  • * Systems near criticality exhibit complex behavior with multiple relevant couplings and fixed points.
  • * Understanding the connections between these fixed points is crucial for characterizing system behavior.

Purpose of the Study:

  • * To present a simple and physically appealing characterization of crossover lines and surfaces.
  • * To relate generalized crossover phenomena to the vanishing of a specific renormalization group function.

Main Methods:

  • * Theoretical analysis of Hamiltonians near criticality.
  • * Investigation of renormalization group functions, specifically Z(-1)(t).
  • * Detailed examination of an explicit example using the tetragonal Landau-Ginzburg-Wilson Hamiltonian.

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Main Results:

  • * A method is presented for characterizing crossover lines and surfaces connecting nontrivial fixed points.
  • * Generalized crossover is shown to be associated with the vanishing of the renormalization group function Z(-1)(t).
  • * The tetragonal Landau-Ginzburg-Wilson Hamiltonian serves as a concrete illustration of the proposed framework.

Conclusions:

  • * The proposed characterization provides a clear framework for understanding complex systems near criticality.
  • * The link between generalized crossover and the vanishing Z(-1)(t) function offers new theoretical insights.
  • * The study validates the approach with a relevant physical model, paving the way for further applications.