Brazilian Journal of Probability and Statistics

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

Aernout C. D. van Enter, Christof Külske, Alex A. Opoku, and Wioletta M. Ruszel

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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.

Article information

Source
Braz. J. Probab. Stat., Volume 24, Number 2 (2010), 226-255.

Dates
First available in Project Euclid: 20 April 2010

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1271770270

Digital Object Identifier
doi:10.1214/09-BJPS029

Mathematical Reviews number (MathSciNet)
MR2643565

Zentralblatt MATH identifier
1200.82015

Keywords
Gibbs measures non-Gibbsian measures n-vector lattice models n-vector mean-field models transformed model Dobrushin uniqueness cluster expansion spin-flop transitions

Citation

van Enter, Aernout C. D.; Külske, Christof; Opoku, Alex A.; Ruszel, Wioletta M. Gibbs–non-Gibbs properties for n -vector lattice and mean-field models. Braz. J. Probab. Stat. 24 (2010), no. 2, 226--255. doi:10.1214/09-BJPS029. https://projecteuclid.org/euclid.bjps/1271770270


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