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This study proves phase transitions in hard-core lattice particle systems using Pirogov-Sinai theory. It also demonstrates a nonzero radius of convergence for the Gaunt-Fisher expansion of pressure.

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Area of Science:

  • Statistical Mechanics
  • Mathematical Physics
  • Condensed Matter Theory

Background:

  • Hard-core lattice particle systems are fundamental models in statistical mechanics.
  • Understanding phase transitions and thermodynamic properties is crucial for these systems.
  • Pirogov-Sinai theory provides a powerful framework for studying phase transitions.

Purpose of the Study:

  • To extend Pirogov-Sinai theory to a general class of hard-core lattice particle systems.
  • To rigorously prove the existence of phase transitions corresponding to sublattice orderings.
  • To analyze the convergence properties of the Gaunt-Fisher expansion for these systems.

Main Methods:

  • Application of an extended Pirogov-Sinai theory.
  • Analysis of systems with a finite number of perfect coverings.
  • Investigation of the Gaunt-Fisher expansion of pressure in powers of inverse fugacity.

Main Results:

  • Phase transitions, linked to sublattice orderings, are proven for a general class of hard-core lattice particle systems.
  • The results encompass many previously studied cases.
  • A nonzero radius of convergence is established for the Gaunt-Fisher expansion of pressure, excluding an explicit logarithmic term.

Conclusions:

  • The extended Pirogov-Sinai theory successfully proves phase transitions in diverse hard-core lattice particle systems.
  • The findings contribute to a deeper understanding of the thermodynamic behavior and convergence properties of these models.
  • This work validates and extends existing results in the field of statistical physics.