Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory

@article{Enter1993RegularityPA,
  title={Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory},
  author={van Aernout Enter and Roberto Fern{\'a}ndez and Alan D. Sokal},
  journal={Journal of Statistical Physics},
  year={1993},
  volume={72},
  pages={879-1167}
}
We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Our main results apply to local (in position space) RG maps acting on systems of bounded spins (compact single-spin space). Regarding regularity, we show that the RG map, defined on a suitable space of interactions (=formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of… CONTINUE READING

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