Phase transition for loop representations of Quantum spin systems on trees

Volker Betz, Johannes Ehlert, Benjamin T Lees

Research output: Contribution to journalArticle (Academic Journal)


We consider a model of random loops on Galton-Watson trees with an offspring distribution with high expectation. We give the configurations a weighting of θ#loops. For many θ > 1, these models are equivalent to certain quantum spin systems for various choices of the system parameters. We find conditions on the offspring distribution that guarantee the occurrence of a phase transition from finite to infinite loops for the Galton-Watson tree.
Original languageEnglish
Number of pages13
JournalJournal of Mathematical Physics
Publication statusPublished - 2018


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