Related papers: Typical sofic entropy and local limits for free gr…

Recent numerical simulations indicate that several different equilibrium glass transitions may be characterized by diverging correlation lengths, and that these divergences are described by a non-mean-field, Ising-like, critical exponent. I…

Let $G$ be a finitely generated amenable group. We study the space of shifts on $G$ over a given finite alphabet $A$. We show that the zero entropy shifts are generic in this space, and that more generally the shifts of entropy $c$ are…

We show that if a closed manifold M admits an F-structure (possibly of rank 0) then its minimal entropy vanishes. In particular, this is the case if M admits a non-trivial circle action. As a corollary we obtain that the simplicial volume…

We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…

We give a new type of sufficient condition for the existence of measures with maximal entropy for an interval map $f$, using some non-uniform hyperbolicity to compensate for a lack of smoothness of $f$. More precisely, if the topological…

We investigate the nature of the critical behaviour of the random-anisotropy Heisenberg model (RAM), which describes a magnetic system with random uniaxial single-site anisotropy, such as some amorphous alloys of rare earths and transition…

Consider a H\"older continuous potential $\phi$ defined on the full shift $A^\nn$, where $A$ is a finite alphabet. Let $X\subset A^\nn$ be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$…

We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ${\mathbb Z}^d$. This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is…

We study the convergence of the density of states and thermodynamic properties in three flat-histogram simulation methods, the Wang-Landau (WL) algorithm, the 1/t algorithm, and tomographic sampling (TS). In the first case the refinement…

We introduce a modification of Voiculescu's free entropy which coincides with the liminf variant of Voiculescu's free entropy on extremal states, but is a concave upper semi-continuous function on the trace state space. We also extend the…

We consider partially hyperbolic diffeomorphisms $f$ with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of…

We study the critical behavior of a general class of cubic-symmetric spin systems in which disorder preserves the reflection symmetry $s_a\to -s_a$, $s_b\to s_b$ for $b\not= a$. This includes spin models in the presence of random…

Let $f:M\rightarrow M$ be a $C^1$ diffeomorphism with a dominated splitting on a compact Riemanian manifold $M$ without boundary. We state and prove several sufficient conditions for the topological entropy of $f$ to be positive. The…

Residual entropy is a key feature associated with emergence in many-body systems. From a variety of frustrated magnets to the onset of spin-charge separation in Hubbard models and fermion-$Z_2$-flux variables in Kitaev models, the freezing…

In 1987, Ornstein and Weiss discovered that the Bernoulli $2$-shift over the rank two free group factors onto the seemingly larger Bernoulli $4$-shift. With the recent creation of an entropy theory for actions of sofic groups (in particular…

We study the residual entropy of a two-dimensional Ising model with crossing and four-spin interactions, both for the case that in zero magnetic field and that in an imaginary magnetic field i({\pi}/2)kT. The spin configurations of this…

Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…

Pseudo entropy is an interesting quantity with a simple gravity dual, which generalizes entanglement entropy such that it depends on both an initial and a final state. Here we reveal the basic properties of pseudo entropy in quantum field…

The eigenstate entanglement entropy has been recently shown to be a powerful tool to distinguish integrable from generic quantum-chaotic models. In integrable models, a unique feature of the average eigenstate entanglement entropy (over all…

We report on tensor renormalization group calculations of entanglement entropy in one-dimensional quantum systems. The reduced density matrix of a Gibbs state can be represented as a $1 + 1$-dimensional tensor network, which is analogous to…