Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published May 2019 | Accepted Version
Journal Article Open

Statistical physics on a product of trees


Let G be the product of finitely many trees T₁ × T₂ × ⋯ × T_N, each of which is regular with degree at least three. We consider Bernoulli bond percolation and the Ising model on this graph, giving a short proof that the model undergoes a second order phase transition with mean-field critical exponents in each case. The result concerning percolation recovers a result of Kozma (2013), while the result concerning the Ising model is new. We also present a new proof, using similar techniques, of a lemma of Schramm concerning the decay of the critical two-point function along a random walk, as well as some generalizations of this lemma.

Additional Information

© 2019 Institut Henri Poincaré. Received: 13 December 2017; Revised: 17 March 2018; Accepted: 13 April 2018; Published: May 2019. First available in Project Euclid: 14 May 2019. We thank Aran Raoufi for help with some references and for spotting a typo, and thank the anonymous referee for suggesting various minor improvements.

Attached Files

Accepted Version - 1712.04911.pdf


Files (183.0 kB)
Name Size Download all
183.0 kB Preview Download

Additional details

August 19, 2023
October 23, 2023