Some numerical results on the block spin transformation for the 2D Ising model at the critical point.

DOI10.1007/BF02183686zbMath1080.82509arXivcond-mat/9404030OpenAlexW3100617055MaRDI QIDQ1593192

G. Benfatto, Enzo Olivieri, Enzo Marinari

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/cond-mat/9404030

zbMATH Keywords

renormalization groupcritical pointIsing modelfinite-size conditions

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) Software, source code, etc. for problems pertaining to statistical mechanics (82-04)

Related Items (9)

Renormalizing the renormalization group pathologies ⋮ Absence of renormalization group pathologies near the critical temperature. Two examples ⋮ Majority rule at low temperatures on the square and triangular lattices ⋮ Effect of the block-spin configuration on the location of \(\beta_c\) in two-dimensional Ising models ⋮ Renormalization group at criticality and complete analyticity of constrained models: A numerical study ⋮ Graded cluster expansion for lattice systems ⋮ 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.

Cites Work

• Approach to equilibrium of Glauber dynamics in the one phase region. I: The attractive case
• Approach to equilibrium of Glauber dynamics in the one phase region. II: The general case
• For 2-D lattice spin systems weak mixing implies strong mixing
• Projections of Gibbs measures may be non-Gibbsian
• Completely analytical interactions: Constructive description
• Block-spins interactions in the Ising model
• A note on the projection of Gibbs measures
• 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
• 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
• Prescribing a System of Random Variables by Conditional Distributions
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