相关论文: KMS states on the C*-algebras of reducible graphs

In this paper, we study KMS states for the gauge actions on C${}^*$-algebras associated with self-similar sets whose branch points are finite. If the self-similar set does not contain any branch point, the Hutchinson measure gives the…

Each multiplicative real-valued homomorphism on a quasi-lattice ordered monoid gives rise to a quasi-periodic dynamics on the associated Toeplitz C*-algebra; here we study the KMS equilibrium states of the resulting C*-dynamical system. We…

We associate with the ring $R$ of algebraic integers in a number field a C*-algebra $\cT[R]$. It is an extension of the ring C*-algebra $\cA[R]$ studied previously by the first named author in collaboration with X.Li. In contrast to…

We consider quantum (unitary) continuous time evolution of spins on a lattice together with quantum evolution of the lattice itself. In physics such evolution was discussed in connection with quantum gravity. It is also related to what is…

We describe KMS-states on the C*-algebras of etale groupoids in terms of measurable fields of traces on the C*-algebras of the isotropy groups. We use this description to analyze tracial states on the transformation groupoid C*-algebras and…

We prove that at any inverse temperature $\beta$ and on any transitive amenable graph, the automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex combinations of the plus and minus states. This is obtained for a…

We introduce a divisibility-type condition for directed graphs that is necessary for $\mathcal{Z}$-stability of the corresponding graph $C^*$-algebra. We prove that this condition is sufficient if either the graph $E$ has no cycles or the…

We exhibit a one-parameter group of automorphism on the Cuntz-algebra O_2 such that the simplex of KMS states changes abruptly at a certain critical temperature from infinitely many to one, and then none. The factor types of the extremal…

We analyze the free energy and construct the Gibbs-KMS states for a class of quantum lattice systems, at low temperatures and when the interactions are almost diagonal in a suitable basis. We study systems with continuous symmetry, but our…

We generalise recent results of Afsar, Larsen and Neshveyev for product systems over quasi-lattice orders by showing that the equilibrium states of quasi-free dynamics on the Nica-Toeplitz $C^*$-algebras of product systems over right LCM…

We determine the factor generated by the GNS-representation defined by a KMS-weight for a generalized gauge action on a simple graph C*-algebra when the corresponding measure on the path space of the graph is conservative for the shift.…

We consider the graph dynamical systems known as k-reversible processes. In such processes, each vertex in the graph has one of two possible states at each discrete time step. Each vertex changes its state between the current time and the…

We address the classification problem for graph $C^*$-algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent special case. Contrasting earlier work, we do not assume that…

We introduce a new model of background independent physics in which the degrees of freedom live on a complete graph and the physics is invariant under the permutations of all the points. We argue that the model has a low energy phase in…

We show that the group ${\mathbb Q \rtimes \mathbb Q^*_+}$ of orientation-preserving affine transformations of the rational numbers is quasi-lattice ordered by its subsemigroup ${\mathbb N \rtimes \mathbb N^\times}$. The associated Toeplitz…

We study the metastability of the ferromagnetic Ising model on a random $r$-regular graph in the zero temperature limit. We prove that in the presence of a small positive external field the time that it takes to go from the all minus state…

A Mauldin-Williams graph $\mathcal{M}$ is a generalization of an iterated function system by a directed graph. Its invariant set $K$ plays the role of the self-similar set. We associate a $C^{*}$-algebra $\mathcal{O}_{\mathcal{M}}(K)$ with…

We introduce a generalisation of Condition (K) to finitely separated graphs and show that it is equivalent to essential freeness of the associated partial action as well as the exchange property of any of the associated tame algebras. As a…

We consider a $W^*$-dynamical system $(\Mg,\taug)$, which models finitely many particles coupled to an infinitely extended heat bath. The energy of the particles can be described by an unbounded operator, which has infinitely many energy…

We explore the recently introduced local-triviality dimensions by studying gauge actions on graph $C^*$-algebras, as well as the restrictions of the gauge action to finite cyclic subgroups. For $C^*$-algebras of finite acyclic graphs and…