Absence of renormalization group pathologies near the critical temperature. Two examples

DOI10.1007/BF02199358zbMath0952.82507MaRDI QIDQ1285149

Tom Kennedy, Karl Haller

Publication date: 18 January 2001

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

zbMATH Keywords

Ising modelDobrushin uniqueness theoremrenormalization group pathologiescompletely analytic potentials

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 (14)

Decimations for one- and two-dimensional Ising and rotator models. II. Continuous vs discrete symmetries ⋮ Decimations for two-dimensional Ising and rotator models ⋮ Effect of self-interaction on the phase diagram of a Gibbs-like measure derived by a reversible probabilistic cellular automata ⋮ Basic Ideas to Approach Metastability in Probabilistic Cellular Automata ⋮ Decimation of the Dyson-Ising ferromagnet ⋮ Gibbsian and non‐Gibbsian states at Eurandom ⋮ Dyson Models Under Renormalization and in Weak Fields ⋮ Renormalizing the renormalization group pathologies ⋮ On regularity of functions of Markov chains ⋮ Renormalization group maps for Ising models in lattice-gas variables ⋮ Weakly Gibbsian measures for lattice spin systems ⋮ Renormalization group transformations near the critical point: Some rigorous results ⋮ Graded cluster expansion for lattice systems ⋮ A cluster expansion approach to renormalization group transformations

Cites Work

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• Approach to equilibrium of Glauber dynamics in the one phase region. I: The attractive case
• Some numerical results on the block spin transformation for the 2D Ising model at the critical point.
• Instability of renormalization-group pathologies under decimation.
• Pathological behavior of renormalization-group maps at high fields and above the transition temperature.
• Ill-defined block-spin transformations at arbitrarily high temperatures.
• Complete analyticity for 2D Ising completed
• On a cluster expansion for lattice spin systems: a finite-size condition for the convergence.
• Cluster expansion for \(d\)-dimensional lattice systems and finite-volume factorization properties.
• Some rigorous results on majority rule renormalization group transformations near the critical point
• Some remarks on pathologies of renormalization-group transformations for the Ising model
• Regularity properties and pathologies of position-space renormalization-group transformations

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