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- Title
Extremes of the internal energy of the Potts model on cubic graphs.
- Authors
Davies, Ewan; Jenssen, Matthew; Perkins, Will; Roberts, Barnaby
- Abstract
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 K 3 , 3's. This proves the d = 3 case of a conjecture of Galvin and Tetali.
- Subjects
POTTS model; GRAPH theory; PATHS &; cycles in graph theory; TEMPERATURE effect; PARTITION functions
- Publication
Random Structures & Algorithms, 2018, Vol 53, Issue 1, p59
- ISSN
1042-9832
- Publication type
Article
- DOI
10.1002/rsa.20767