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This study explores the critical behavior of the two-dimensional spin-1 Baxter-Wu model. Monte Carlo simulations reveal the transition belongs to the four-state Potts model universality class, clarifying critical phenomena.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Phase transitions

Background:

  • The Baxter-Wu model is a significant model in statistical mechanics for studying phase transitions.
  • Understanding universality classes is crucial for classifying critical phenomena across different systems.

Purpose of the Study:

  • To determine the universality class of second-order phase transitions in the two-dimensional spin-1 Baxter-Wu model.
  • To investigate the influence of crystal-field coupling (Δ) on the model's critical behavior.
  • To explore the proximity of the multicritical point.

Main Methods:

  • Extensive Monte Carlo simulations were performed.
  • Analysis of energy probability distribution zeros (Fisher zeros).
  • Application of the multicanonical approach to study crystal-field energy distribution.

Main Results:

  • Finite-size scaling analysis supports the four-state Potts model universality class for second-order transitions.
  • Strong finite-size effects observed for positive crystal-field coupling (Δ) indicate crossover effects.
  • Combined cluster and heat-bath updates improve system equilibration.

Conclusions:

  • The critical behavior of the spin-1 Baxter-Wu model aligns with the four-state Potts model universality class.
  • Crossover effects near the first-order transition line influence critical behavior for Δ > 0.
  • Advanced simulation techniques enhance the study of complex systems and resolve ambiguities.