Extremes of the internal energy of the Potts model on cubic graphs

Ewan Davies, Matthew Jenssen, Will Perkins, Barnaby Roberts

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
189 Downloads (Pure)

Abstract

We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs at every temperature and for all q ≥ 2. This immediately implies corresponding tight bounds on the anti-ferromagnetic Potts partition function. Taking the zero-temperature limit gives new results in extremal combinatorics: the number of q-colorings of a 3-regular graph, for any q ≥ 2, is maximized by a union of K3,3’s. This proves the d = 3 case of a conjecture of Galvin and Tetali.
Original languageEnglish
Pages (from-to)59-75
Number of pages17
JournalRandom Structures and Algorithms
Volume53
Issue number1
Early online date4 Feb 2018
DOIs
Publication statusPublished - Aug 2018

Keywords

  • Potts mode
  • partition function
  • graph colorings
  • graph homomorphims
  • Ising model

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