Phase Transitions on C*-Algebras from Actions of Congruence Monoids on Rings of Algebraic Integers
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Beta 2
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Abstract We compute the KMS (equilibrium) states for the canonical time evolution on C*-algebras from actions of congruence monoids on rings of algebraic integers. We show that for each $\beta \in [1,2]$, there is a unique KMS$_\beta $ state, and we prove that it is a factor state of type III$_1$. There are phase transitions at $\beta =2$ and $\beta =\infty $ involving a quotient of a ray class group. Our computation of KMS and ground states generalizes the results of Cuntz, Deninger, and Laca for the full $ax+b$-semigroup over a ring of integers, and our type classification generalizes a result of Laca and Neshveyev in the case of the rational numbers and a result of Neshveyev in the case of arbitrary number fields.
2019 ◽
Vol 373
(1)
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pp. 699-726
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1992 ◽
Vol 35
(3)
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pp. 295-302
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1983 ◽
Vol 94
(1)
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pp. 23-28
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2015 ◽
Vol 93
(2)
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pp. 199-210
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2011 ◽
Vol 07
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pp. 101-114
2000 ◽
Vol 52
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pp. 47-91
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1991 ◽
Vol 43
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pp. 255-264
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