Related papers: Equilibrium and ground states from Cayley graphs
The paper contains a description of the KMS states and ground states of a generalized gauge action on the C*-algebra of a finite graph.
Given a positive function on the set of edges of an arbitrary directed graph $E=(E^0,E^1)$, we define a one-parameter group of automorphisms on the C*-algebra of the graph $C^*(E)$, and study the problem of finding KMS states for this…
We determine the factor types of the extremal KMS weights for generalized gauge actions on a graph algebra, and the ground states for the restriction of the action to a corner defined from a vertex. The assumptions on the graph and the…
KMS weights for generalized gauge actions on graph C*-algebras are studied and a complete description of the structure is obtained for the gauge action when the graph is strongly connected and has at most countably many exits. The structure…
The relative graph $C^*$-algebras introduced by Muhly and Tomforde are generalizations of both graph algebras and their Toeplitz extensions. For an arbitrary graph $E$ and a subset $R$ of the set of regular vertices of $E$ we show that the…
We describe the KMS-states and the ground states for the gauge action on the C*-algebra of the oriented transformation groupoid of a continuous piecewise monotone and exact map of the circle.
We consider operator-algebraic dynamical systems given by actions of the real line on unital $C^*$-algebras, and especially the equilibrium states (or KMS states) of such systems. We are particularly interested in systems built from the…
We describe the structure of ground states and ceiling states for generalized gauge actions on an UHF algebra. It is shown that both sets are affinely homeomorphic to the state space of a unital AF algebra, and that any pair of unital AF…
We consider a finite directed graph E, and the gauge action on its Toeplitz-Cuntz-Krieger algebra, viewed as an action of R. For inverse temperatures larger than a critical value \beta_c, we give an explicit construction of all the…
We study the KMS states of the C*-algebra of a strongly connected finite k-graph. We find that there is only one 1-parameter subgroup of the gauge action that can admit a KMS state. The extreme KMS states for this preferred dynamics are…
The paper develops a series of tools for the study of KMS-weights on graph C*-algebras and KMS states on their corners. The approach adopts methods and ideas from graph theory, random walks and dynamical systems.
We completely classify the KMS states for the gauge action on a $C^*$-algebra associated with a rational function $R$ introduced in our previous work. The gauge action has a phase transition at $\beta = \log \deg R$. We can recover the…
We describe KMS and ground states arising from a generalized gauge action on ultragraph C*-algebras. We focus on ultragraphs that satisfy Condition~(RFUM), so that we can use the partial crossed product description of ultragraph C*-algebras…
We consider a family of operator-algebraic dynamical systems involving the Toeplitz algebras of higher-rank graphs. We explicitly compute the KMS states (equilibrium states) of these systems built from small graphs with up to four connected…
Given a self-similar $K$ set defined from an iterated function system $\Gamma=(\gamma_1,\ldots,\gamma_n)$ and a set of function $H=\{h_i:K\to\mathbb{R}\}_{i=1}^d$ satisfying suitable conditions, we define a generalized gauge action on…
We introduce the notion of a self-similar action of a groupoid $G$ on a finite higher-rank graph. To these actions we associate a compactly aligned product system of Hilbert bimodules, and thereby obtain corresponding universal…
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…
We consider self-similar actions of groupoids on the path spaces of finite directed graphs, and construct examples of such self-similar actions using a suitable notion of graph automaton. Self-similar groupoid actions have a Cuntz-Pimsner…
For a finite, strongly connected $k$-graph $\Lambda$, an Huef, Laca, Raeburn and Sims studied the KMS states associated to the preferred dynamics of the $k$-graph $C^*$-algebra $C^*(\Lambda)$. They found that these KMS states are determined…
The paper contains a description of the KMS weights for the one-parameter action on the reduced C*-algebra of a second countable locally compact Hausdorff etale groupoid, arising from a continuous real valued homomorphism satisfying two…