Gibbs-non-Gibbs properties for n-vector lattice and mean-field models

2008/12/09 by Aernout C. D. van Enter, A. C. D. van Enter, van Enter, A. C. D. +9
Mathematics · Physics and Astronomy · #60K35 #82B20 #82B26 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #math.PR #msc:60K35 #msc:82B20 #msc:82B26

paper · pdf · doi:10.48550/arxiv.0812.1751

31 pages, 6 figures

arxiv created 2008/12/09 · openalex publication_date 2008/12/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review some recent developments in the study of Gibbs and non-Gibbs properties of transformed n-vector lattice and mean-field models under various transformations. Also, some new results for the loss and recovery of the Gibbs property of planar rotor models during stochastic time evolution are presented.

Citations

• Mathematical properties of position-space renormalization-group transformations
• Gibbsianness versus Non-Gibbsianness of time-evolved planar rotor models
• Gibbsian and non-Gibbsian states at Eurandom

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• Gibbsianness versus Non-Gibbsianness of time-evolved planar rotor models
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• Dynamical Gibbs-non-Gibbs transitions in Curie-Weiss Widom-Rowlinson models
• Stochastic Stability and the Spin Glass Phase. The State of the Art for Mean Field and Finite Dimensional Models