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Pathological behavior of renormalization-group maps at high fields and above the transition temeprature

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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.

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van Enter, A.C.D., Fernández, R. & Kotecký, R. Pathological behavior of renormalization-group maps at high fields and above the transition temeprature. J Stat Phys 79, 969–992 (1995). https://doi.org/10.1007/BF02181211

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Key Words

  • Non-Gibbsian measures
  • real-space renormalization
  • complete analyticity
  • majority-rule
  • decimation