Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions. I: Cluster expansion

DOI10.1007/BF01225035zbMath0663.60075OpenAlexW2044818053MaRDI QIDQ1114236

Yong Moon Park

Publication date: 1988

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01225035

zbMATH Keywords

low temperaturescluster expansionlattice systems with finite range interactionsPirogov-Sinai theory of phase transitions

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Classical equilibrium statistical mechanics (general) (82B05)

Related Items

Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions. II: Phase diagram ⋮ Extension of the Pirogov-Sinai theory to a class of quasiperiodic interactions ⋮ Stability of uniqueness and coexistence of equilibrium states of the Ising model under long range perturbations ⋮ Interactions and pressure functionals for disordered lattice systems ⋮ Abstract polymer models with general pair interactions ⋮ Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory ⋮ Absence of phase transitions in a class of integer spin systems ⋮ Stability of ground state degeneracy to long-range interactions

Cites Work

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• The cluster expansion for classical and quantum lattice systems
• First order phase transitions in lattice and continuous systems: Extension of Pirogov-Sinai theory
• Cluster expansion for abstract polymer models
• Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions. II: Phase diagram
• The pure phases (harmonic functions) of generalized processes or: Mathematical physics of phase transitions and symmetry breaking
• Existence of a Phase Transition in Two-Dimensional and Three-Dimensional Ising Models
• On Ising's model of ferromagnetism