Supercritical phase transition on the Toeplitz algebra of ${\mathbb N^\times}\ltimes \mathbb{Z}$
Year: 2026
Type: article
Abstract: We study the high-temperature equilibrium for the \mathrm{C}^{*} -algebra \mathcal{T}({\mathbb{N^}\times}\ltimes \mathbb{Z}) recently considered by an Huef, Laca, and Raeburn. We show that the simplex of \mathrm{KMS}_{\beta} states at each inverse temperature \beta in the critical interval (0,1] is a Bauer simplex whose space of extreme points is homeomorphic to \N \sqcup\{\infty\} . This is in contrast to the uniqueness of equilibrium at high temperature observed in previously considered systems arising from number theory. We also show that quotients of our system exhibit spontaneous symmetry breaking by finite cyclotomic Galois groups and establish their connection to the Bost–Connes phase transition.
DOI: 10.4171/jncg/692
Authors: Marcelo Laca, Tyler Schulz
Institution: University of Victoria
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416083498
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