Pathological behavior of renormalization-group maps at high fields and above the transition temperature.

DOI10.1007/BF02181211zbMath1081.82558arXivhep-lat/9409016MaRDI QIDQ1593246

Aernout C. D. van Enter, Roberto Fernández, Roman Kotecký

Publication date: 16 January 2001

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-lat/9409016

zbMATH Keywords

decimationmajority-rulenon-Gibbsian measurescomplete analyticityreal-space renormalization

Mathematics Subject Classification ID

Renormalization group methods in equilibrium statistical mechanics (82B28) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (10)

Critical phenomena and renormalization-group theory ⋮ Decimations for one- and two-dimensional Ising and rotator models. II. Continuous vs discrete symmetries ⋮ Decimations for two-dimensional Ising and rotator models ⋮ Renormalizing the renormalization group pathologies ⋮ Weakly Gibbsian measures for lattice spin systems ⋮ Absence of renormalization group pathologies near the critical temperature. Two examples ⋮ Majority rule at low temperatures on the square and triangular lattices ⋮ Renormalization group at criticality and complete analyticity of constrained models: A numerical study ⋮ Ill-defined block-spin transformations at arbitrarily high temperatures. ⋮ Almost sure quasilocality fails for the random-cluster model on a tree.

Cites Work

• First order phase transitions in lattice and continuous systems: Extension of Pirogov-Sinai theory
• Gibbs measures and phase transitions
• Correlation inequalities on some partially ordered sets
• Some numerical results on the block spin transformation for the 2D Ising model at the critical point.
• Instability of renormalization-group pathologies under decimation.
• Completely analytical interactions: Constructive description
• A note on the projection of Gibbs measures
• Some rigorous results on majority rule renormalization group transformations near the critical point
• Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory
• Some remarks on pathologies of renormalization-group transformations for the Ising model
• Classification of Gibbs' states on Smale spaces and one-dimensional lattice systems
• Unnamed Item

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