Almost Gibbsianness and parsimonious description of the decimated 2d-Ising model

DOI10.1007/s10955-013-0773-1zbMath1280.82005OpenAlexW1968983935MaRDI QIDQ368672

Arnaud Le Ny

Publication date: 23 September 2013

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

Full work available at URL: https://doi.org/10.1007/s10955-013-0773-1

zbMATH Keywords

renormalizationIsing modelDobryshin programDobryshin-Lanford-Ruelle approachgeneralized Gibbs measures

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

Decimations for two-dimensional Ising and rotator models ⋮ Decimation of the Dyson-Ising ferromagnet ⋮ Dyson Models Under Renormalization and in Weak Fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Infinite systems of interacting chains with memory of variable length -- a stochastic model for biological neural nets
• Partially observed Markov random fields are variable neighborhood random fields
• A finite-volume version of Aizenman-Higuchi theorem for the 2D Ising model
• Neighborhood radius estimation for variable-neighborhood random fields
• Remarks on the global Markov property
• Gibbs measures and phase transitions
• Random fields
• Sufficient statistics and extreme points
• Renormalization group pathologies and the definition of Gibbs states
• Transformations of Gibbs measures
• ``Non-Gibbsian states and their Gibbs description
• Hydrodynamics for quasi-free quantum systems
• Variational principle for some renormalized measures
• Global specifications and nonquasilocality of projections of Gibbs measures
• Relative energies for non-Gibbsian states
• Almost Gibbsian versus weakly Gibbsian measures
• (Almost) Gibbsian description of the sign fields of SOS fields
• Projections of Gibbs measures may be non-Gibbsian
• Variational principle and almost quasilocality for renormalized measures
• Relative entropy and variational properties of generalized Gibbsian measures.
• Complete analyticity for 2D Ising completed
• Quite weak Bernoulli with exponential rate and percolation for random fields
• Percolation, path large deviations and weakly Gibbs states
• Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory
• Potentials for almost Markovian random fields
• Course 15 Gibbsianness and non-gibbsianness in lattice random fields
• Introduction to (generalized) Gibbs measures
• A universal data compression system
• Existence of compatible families of proper regular conditional probabilities
• A note on specifications
• Beitrag zur Theorie des Ferromagnetismus
• On Ising's model of ferromagnetism
• Observables at infinity and states with short range correlations in statistical mechanics