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A HIGH-TEMPERATURE PHASE TRANSITION FROM NUMBER THEORY
- Speaker(s)
- MARCELO LACA
- Affiliation
- University of Victoria, Canada
- Language of the talk
- English
- Date
- March 5, 2025, 5:15 p.m.
- Information about the event
- IMPAN 405 & ZOOM
- Title in Polish
- A HIGH-TEMPERATURE PHASE TRANSITION FROM NUMBER THEORY
- Seminar
- North Atlantic Noncommutative Geometry Seminar
Let S be the semidirect product of the multiplicative positive integers acting on the integers, with the operation (a,m)(b,n) = (ab,bm+n), where a and b are positive. In previous joint work with Astrid an Huef and Iain Raeburn, we studied the Toeplitz C*-algebra generated by the left regular representation of S on l^2(S), and showed that the extremal KMS equilibrium states with respect to the natural dynamics, for inverse temperatures above the critical value 1, are parametrized by the point masses on the unit circle. I will talk about what happens for inverse temperatures between 0 and 1. Surprisingly, the system has an unprecedented high-temperature phase transition with extremal KMS states parametrized by averages of point masses at roots of unity of the same primitive order together with Lebesgue measure. The quotients associated to these extremal states embed in the Bost-Connes algebra, and establish a link to the Bost-Connes phase transition with spontaneous symmetry breaking. This is current joint work with Tyler Schulz.
