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E Can Artun1, A Nihat Berker1,2

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Researchers calculated the critical sizes of metastable droplets and hysteresis loops in q-state Potts models. This finite-system renormalization-group theory approach reveals how magnetic fields and temperature influence these properties.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Metastable states are crucial in understanding phase transitions.
  • The q-state Potts model is a fundamental framework for studying magnetism and phase transitions.

Purpose of the Study:

  • To calculate the existence and limits of metastable droplets in q-state Potts models.
  • To determine the dependence of droplet critical sizes and hysteresis loops on system parameters.
  • To explore the applicability of the method to other metastable systems.

Main Methods:

  • Utilizing finite-system renormalization-group theory.
  • Applying the method to q-state Potts models in three spatial dimensions (d=3).
  • Analyzing the impact of magnetic field, temperature, and the number of Potts states (q).

Main Results:

  • Calculated critical droplet sizes and their dependence on magnetic field, temperature, and q.
  • Deduced hysteresis loop sizes and shapes across first-order phase transitions.
  • Observed and noted asymmetry in hysteresis loop branches.

Conclusions:

  • The finite-system renormalization-group theory effectively models metastable droplet properties and hysteresis.
  • The findings provide insights into phase transitions in magnetic systems.
  • The method's potential extension to surface-adsorbed systems and water is highlighted.