Infinite-volume states with irreducible localization sets for gradient models on trees

HIGHLIGHTS

• What: As a further application of the method the authors obtain the existence of new types of gradient Gibbs states with Z-valued spins whose single-site marginals do not localize but whose correlation structure depends on the finite set A where the authors provide explicit expressions for the correlation between the height-increments along disjoint edges. For the latter the authors devise a suitable (conditional) map on sequence space which A. Abbondandolo et_al the authors show to be a contraction, for the former the authors employ the Brouwer fixed point theorem, see_(42). The authors show . . .
  

   

  

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