Pathological Behavior of Renormalization-Group Maps at High Fields and Above the Transition Temperature

1994/09/20 by Aernout C. D. van Enter, van Enter, Aernout C. D., Roberto Fernández +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Markov Chains and Monte Carlo Methods #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #hep-lat

paper · pdf · doi:10.48550/arxiv.hep-lat/9409016

24 pages

arxiv created 1994/09/20 · openalex publication_date 1994/09/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the Ising model in a very strong field at low temperatures produce non-Gibbsian measures. This shows that pathological behavior of renormalization-group transformations is even more widespread than previous examples already suggested.

Citations

• Mathematical properties of position-space renormalization-group transformations

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