Weakly Gibbsian measures for lattice spin systems

DOI10.1007/BF02765536zbMath0939.82012OpenAlexW2004233504MaRDI QIDQ1285121

Christian Maes, József Lörinczi

Publication date: 11 July 2000

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

Full work available at URL: https://doi.org/10.1007/bf02765536

zbMATH Keywords

transformationsGibbs measureslattice spin systemsrenormalization group pathologiesweakly Gibbsian measuresweakly Gibbsian states

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) 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 (2)

Almost Gibbsian versus weakly Gibbsian measures ⋮ A cluster expansion approach to renormalization group transformations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gibbs measures and phase transitions
• Random fields
• Absence of renormalization group pathologies near the critical temperature. Two examples
• Relative energies for non-Gibbsian states
• Almost sure quasilocality in the random cluster model.
• Pathological behavior of renormalization-group maps at high fields and above the transition temperature.
• Agreement percolation and phase coexistence in some Gibbs systems.
• Ill-defined block-spin transformations at arbitrarily high temperatures.
• Almost sure quasilocality fails for the random-cluster model on a tree.
• Projections of Gibbs measures may be non-Gibbsian
• Quite weak Bernoulli with exponential rate and percolation for random fields
• A note on the projection of Gibbs measures
• Exponential decay of connectivities in the two-dimensional Ising model
• The stochastic random-cluster process and the uniqueness of random-cluster measures
• Statistical mechanics of probabilistic cellular automata.
• Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory
• Superstable interactions in classical statistical mechanics
• Potentials for almost Markovian random fields
• The fuzzy Potts model
• Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
• Almost sure entropy and the variational principle for random fields with unbounded state space
• Robustness of the non-Gibbsian property: some examples
• Statistical mechanics of image restoration

This page was built for publication: Weakly Gibbsian measures for lattice spin systems