A symmetry breaking transition in the edge/triangle network model
Annales de l’Institut Henri Poincaré D, Tome 5 (2018) no. 2, pp. 251-286.

Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp transition between two phases with different symmetries, analogous to the transition between a fluid and a crystalline solid.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/54
Classification : 05-XX, 82-XX
Mots-clés : Graph limits, entropy, bipodal structure, phase transitions, symmetry breaking 
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Radin, Charles; Ren, Kui; Sadun, Lorenzo. A symmetry breaking transition in the edge/triangle network model. Annales de l’Institut Henri Poincaré D, Tome 5 (2018) no. 2, pp. 251-286. doi : 10.4171/aihpd/54. https://www.numdam.org/articles/10.4171/aihpd/54/
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  • Kenyon, Richard; Radin, Charles; Ren, Kui; Sadun, Lorenzo The phases of large networks with edge and triangle constraints, Journal of Physics A: Mathematical and Theoretical, Volume 50 (2017) no. 43 | DOI:10.1088/1751-8121/aa8ce1
  • Radin, Charles; Ren, Kui; Sadun, Lorenzo Surface effects in dense random graphs with sharp edge constraint, arXiv (2017) | DOI:10.48550/arxiv.1709.01036 | arXiv:1709.01036
  • Radin, Charles Wulff shape for equilibrium phases, arXiv (2016) | DOI:10.48550/arxiv.1610.08564 | arXiv:1610.08564

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