KMS states and conformal measures

TL;DR

This paper links KMS states in groupoid C*-algebras to conformal measures from complex dynamics, revealing phase transitions in quantum statistical models derived from quadratic polynomials.

Contribution

It constructs a groupoid C*-algebra framework connecting holomorphic maps, conformal measures, and KMS states, illustrating phase transitions in quantum models.

Findings

KMS states correspond to conformal measures

Quadratic polynomials induce phase transitions

Quantum statistical models exhibit spontaneous symmetry breaking

Abstract

From a non-constant holomorphic map on a connected Riemann surface we construct an 'etale second countable locally compact Hausdorff groupoid whose associated groupoid C*-algebra admits a one-parameter group of automorphisms with the property that its KMS states corresponds to conformal measures in the sense of Sullivan. In this way certain quadratic polynomials give rise to quantum statistical models with a phase transition arising from spontaneous symmetry breaking.