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Star-graph expansions for bond-diluted Potts models.

Meik Hellmund1, Wolfhard Janke

  • 1Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany. Meik.Hellmund@itp.uni-leipzig.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
Summary

Researchers analyzed random-bond Potts models using series expansions. They found evidence that disorder can change a first-order phase transition to a second-order one in the four-state Potts model.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Computational physics

Background:

  • The behavior of disordered systems is crucial in condensed matter physics.
  • Understanding phase transitions in models like the Potts model is a key research area.
  • Previous studies on the Potts model often focused on undiluted or simpler cases.

Purpose of the Study:

  • To develop a method for calculating properties of random-bond Potts models with arbitrary disorder.
  • To investigate the influence of quenched disorder on phase transitions.
  • To analyze the parameter space of disorder strength and lattice dimension.

Main Methods:

  • Derivation of high-temperature series expansions for free energy and susceptibility.
  • Application of a star-graph expansion technique for exact disorder averaging.

Related Experiment Videos

  • Analysis of series expansions using various techniques to explore parameter space.
  • Focus on the bond-diluted four-state Potts model in d=3.

    • Main Results:

    • Exact calculation of quenched disorder averages for arbitrary coupling distributions.
    • Development of a method applicable to symbolic disorder strength (p) and dimension (d).
    • Results for transition temperature and critical exponent gamma as a function of disorder (p) up to order 18.
    • Observation of signals for a softening from first-order to second-order transition.

    Conclusions:

    • The star-graph expansion technique provides a powerful tool for studying disordered systems.
    • Finite disorder strength appears to induce a change in the nature of the phase transition in the four-state Potts model.
    • The findings align with and provide further evidence for recent Monte Carlo simulations.