C. Garban: Long-range order for critical Book-Ising and Book-percolation

Abstract: This talk will focus on the behaviour of statistical physics models on a book with pages isomorphic to half-planes. We will show that even for models undergoing a continuous phase transition on \mathbb Z^2, the phase transition becomes discontinuous as soon as the number of pages is sufficiently large. In particular, we prove that:

  1. the Ising model on a three pages book has a discontinuous phase transition
  2. standard i.i.d percolation on a four pages book has an infinite cluster at p_c=\tfrac12

These results confirm predictions in theoretical physics which relied on renormalization group, conformal field theory and numerics, some of which were motivated by the analysis of the Renyi entropy of certain quantum spin systems.

This is a joint work with Hugo Duminil-Copin and Vincent Tassion.


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