Supercritical phase transition on the Toeplitz algebra of $\mathbb N^\times \ltimes \mathbb Z$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909830457851904 |
|---|---|
| author | Laca, Marcelo Schulz, Tyler |
| author_facet | Laca, Marcelo Schulz, Tyler |
| contents | We study the high-temperature equilibrium for the C*-algebra $\mathcal T (\mathbb N^\times \ltimes \mathbb N)$ recently considered by an Huef, Laca and Raeburn. We show that the simplex of KMS$_β$ states at each inverse temperature $β$ in the critical interval $(0,1]$ is a Bauer simplex whose space of extreme points is homeomorphic to $\mathbb N \sqcup\{\infty\}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supercritical phase transition on the Toeplitz algebra of $\mathbb N^\times \ltimes \mathbb Z$ Laca, Marcelo Schulz, Tyler Operator Algebras Number Theory 45L05, 46L55 We study the high-temperature equilibrium for the C*-algebra $\mathcal T (\mathbb N^\times \ltimes \mathbb N)$ recently considered by an Huef, Laca and Raeburn. We show that the simplex of KMS$_β$ states at each inverse temperature $β$ in the critical interval $(0,1]$ is a Bauer simplex whose space of extreme points is homeomorphic to $\mathbb N \sqcup\{\infty\}$. 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. |
| title | Supercritical phase transition on the Toeplitz algebra of $\mathbb N^\times \ltimes \mathbb Z$ |
| topic | Operator Algebras Number Theory 45L05, 46L55 |
| url | https://arxiv.org/abs/2503.03033 |