A HIGH-TEMPERATURE PHASE TRANSITION FROM NUMBER THEORY

Prelegent(ci)

MARCELO LACA

Afiliacja

University of Victoria, Canada

Język referatu

angielski

Termin

5 marca 2025 17:15

Informacje na temat wydarzenia

IMPAN 405 & ZOOM

Tytuł w języku polskim

A HIGH-TEMPERATURE PHASE TRANSITION FROM NUMBER THEORY

Seminarium

North Atlantic Noncommutative Geometry Seminar

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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.

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