Mathematics – Operator Algebras
Scientific paper
2011-09-11
Mathematics
Operator Algebras
Typos fixed and the last section revised
Scientific paper
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.
Thomsen Klaus
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