Some remarks on pathologies of renormalization-group transformations for the Ising model

DOI10.1007/BF01048184zbMath1101.82312MaRDI QIDQ2499893

Fabio Martinelli, Enzo Olivieri

Publication date: 23 August 2006

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

zbMATH Keywords

non-GibbsiannessDecimationFinite-size conditionsRenormalization-group

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 (16)

Decimations for one- and two-dimensional Ising and rotator models. II. Continuous vs discrete symmetries ⋮ For 2-D lattice spin systems weak mixing implies strong mixing ⋮ A note on the projection of Gibbs measures ⋮ Global specifications and nonquasilocality of projections of Gibbs measures ⋮ Absolute continuity of non-homogeneous Gibbs measures of the Ising model on the Cayley tree ⋮ Renormalizing the renormalization group pathologies ⋮ Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory ⋮ Invariant manifolds associated to nonresonant spectral subspaces ⋮ Absence of renormalization group pathologies near the critical temperature. Two examples ⋮ Renormalization group at criticality and complete analyticity of constrained models: A numerical study ⋮ Renormalization group transformations near the critical point: Some rigorous results ⋮ 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. ⋮ A cluster expansion approach to renormalization group transformations

Cites Work

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• Cluster expansion for \(d\)-dimensional lattice systems and finite-volume factorization properties.
• Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory
• Crystalline variational problems

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