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Generalized Gibbs Phase Rule and Multicriticality Applied to Magnetic Systems.

Daniele A Dias1, Francisco W S Lima2, Joao A Plascak3,4,5

  • 1Campus Patos de Minas, Universidade Federal de Uberlândia, Patos de Minas 38700-103, Brazil.

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Summary
This summary is machine-generated.

A generalized Gibbs phase rule helps understand phase diagrams in magnetic models by counting degrees of freedom. This new rule describes critical points and phase coexistence in models like Ising and Potts.

Keywords:
Gibbs phase rulemagnetic systemsphase diagrams

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Thermodynamics

Background:

  • The Gibbs phase rule is fundamental for understanding phase diagrams in physical systems.
  • Lattice spin magnetic models exhibit complex phase behavior, including coexistence and multicritical phenomena.
  • Existing phase rules may not fully capture the intricacies of these magnetic models.

Purpose of the Study:

  • To generalize the Gibbs phase rule for analyzing phase diagrams in lattice spin magnetic models.
  • To investigate single-phase regions, multiphase coexistence, and multicritical phenomena.
  • To provide a framework for understanding the topology of phase diagrams in magnetic systems.

Main Methods:

  • Developing a generalized Gibbs phase rule based on thermodynamic degrees of freedom.
  • Analyzing the influence of external fields on ground state degeneracy.
  • Applying the generalized rule to specific models: Ising, Blume-Capel, and q-state Potts models.

Main Results:

  • The generalized Gibbs phase rule successfully describes the possible topology of phase diagrams for various spin models.
  • External fields are crucial for breaking ground state degeneracy and defining degrees of freedom.
  • The rule accurately predicts the presence of critical and multicritical surfaces and isolated points.

Conclusions:

  • The generalized Gibbs phase rule offers a valuable tool for characterizing phase diagram topology in magnetic models.
  • While not locating phase boundaries, it effectively describes potential critical and multicritical phenomena.
  • This approach enhances the understanding of phase transitions in condensed matter systems.