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Constrained tricritical phenomena in two dimensions.

Youjin Deng1, Jouke R Heringa, Henk W J Blöte

  • 1Laboratory for Material Science, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
Summary

We studied tricritical models using Monte Carlo simulations. Constraining vacancies modifies critical behavior, changing specific heat and structure factor exponents as explained by Fisher renormalization.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Computational physics

Background:

  • Tricritical models exhibit complex phase transitions.
  • Understanding critical phenomena requires advanced simulation techniques.
  • Lattice models with constraints present unique theoretical challenges.

Purpose of the Study:

  • Investigate tricritical models (Blume-Capel, hard-square, Potts with vacancies) on a square lattice.
  • Analyze the impact of vacancy constraints on critical singularities.
  • Explain observed phenomena using generalized Fisher renormalization.

Main Methods:

  • Monte Carlo simulations utilizing Wolff and geometric cluster algorithms.
  • Sampling of specific heat (C) and structure factor (C(s)).

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  • Preservation of total vacancy count to mitigate critical slowing down.

    • Main Results:

    • Specific heat (C) becomes finite at tricriticality under constraint.
    • Structure factor (C(s)) remains divergent, similar to unconstrained systems.
    • Leading thermal exponent y(t1) is renormalized to 2-y(t1); subleading y(t2) is unchanged.

    Conclusions:

    • Vacancy constraints significantly alter critical singularities in tricritical models.
    • Generalized Fisher renormalization successfully explains these constrained phenomena.
    • The study provides insights into the role of scaling fields in critical behavior.