Global specifications and nonquasilocality of projections of Gibbs measures

DOI10.1214/aop/1024404514zbMath0895.60096OpenAlexW2024049619MaRDI QIDQ1370220

Roberto Fernández, Charles-Edouard Pfister

Publication date: 26 October 1997

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1024404514

zbMATH Keywords

Ising modelrandom fieldsGibbs measuresglobal Markov propertydecimation processesdiscontinuity of conditional probabilitiesmonotonicity preserving specificationsnonquasilocalityprojections of measures

Mathematics Subject Classification ID

Random fields (60G60) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Classical equilibrium statistical mechanics (general) (82B05) Renormalization group methods in equilibrium statistical mechanics (82B28) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Markov processes (60J99)

Related Items (19)

Decimations for one- and two-dimensional Ising and rotator models. II. Continuous vs discrete symmetries ⋮ Decimations for two-dimensional Ising and rotator models ⋮ Relative entropy and variational properties of generalized Gibbsian measures. ⋮ Graphical representations for Ising and Potts models in general external fields ⋮ Almost Gibbsianness and parsimonious description of the decimated 2d-Ising model ⋮ Decimation of the Dyson-Ising ferromagnet ⋮ Gibbsian and non‐Gibbsian states at Eurandom ⋮ One-sided continuity properties for the schonmann projection ⋮ On the Mathematical Consequences of Binning Spike Trains ⋮ One-Sided Versus Two-Sided Stochastic Descriptions ⋮ Dyson Models Under Renormalization and in Weak Fields ⋮ Renormalizing the renormalization group pathologies ⋮ Propagation of Gibbsianness for infinite-dimensional gradient Brownian diffusions ⋮ Entropic repulsion and lack of the \(g\)-measure property for Dyson models ⋮ Loss and recovery of Gibbsianness for XY models in external fields ⋮ Dynamical Gibbs-non-Gibbs transitions in lattice Widom-Rowlinson models with hard-core and soft-core interactions ⋮ Gibbsianness versus non-Gibbsianness of time-evolved planar rotor models ⋮ Entropy for translation-invariant random-cluster measures ⋮ Almost Gibbsian versus weakly Gibbsian measures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semi-infinite Ising model. II: The wetting and layering transitions.
• Gibbsian random fields for lattice systems with pairwise interactions.
• Remarks on the global Markov property
• Gibbs measures and phase transitions
• Projections of Gibbs measures may be non-Gibbsian
• A note on the projection of Gibbs measures
• The stochastic random-cluster process and the uniqueness of random-cluster measures
• 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
• Potentials for almost Markovian random fields
• Existence of compatible families of proper regular conditional probabilities
• A note on specifications
• Robustness of the non-Gibbsian property: some examples

This page was built for publication: Global specifications and nonquasilocality of projections of Gibbs measures