Published May 2019
| Accepted Version
Journal Article
Open
Statistical physics on a product of trees
- Creators
- Hutchcroft, Tom
Abstract
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
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1712.04911.pdf
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Additional details
- Eprint ID
- 111006
- Resolver ID
- CaltechAUTHORS:20210922-193309508
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2021-09-27Created from EPrint's datestamp field
- Updated
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2021-09-27Created from EPrint's last_modified field