Geometrical mutual information at the tricritical point of the two-dimensional Blume-Capel model

The spin-1 classical Blume-Capel model on a square lattice is known to exhibit a finite-temperature phase transition described by the tricritical Ising CFT in 1+1 space-time dimensions. This phase transition can be accessed with classical Monte Carlo simulations, which, via a replica-trick calculation, can be used to study the shape-dependence of the classical R\'enyi entropies for a torus divided into two cylinders. From the second R\'enyi entropy, we calculate the Geometrical Mutual Information (GMI) introduced by St\'ephan et. al. [Phys. Rev. Lett. 112, 127204 (2014)] and use it to extract a numerical estimate for the value of the central charge near the tricritical point. By comparing to the known CFT result, $c=7/10$, we demonstrate how this type of GMI calculation can be used to estimate the position of the tricritical point in the phase diagram.Comment: version accepted in JSTA

A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) for the purpose of calculating the Renyi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analogue to the density of states for Stochastic Series Expansion QMC allowing a direct calculation of Renyi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, 2D transverse field Ising model, and 3D Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.Comment: 9 pages, 7 figure

Hidden Broad Line Seyfert 2 Galaxies in the CfA and 12micron Samples

We report the results of a spectropolarimetric survey of the CfA and 12micron samples of Seyfert 2 galaxies (S2s). Polarized (hidden) broad line regions (HBLRs) are confirmed in a number of galaxies, and several new cases (F02581-1136, MCG -3-58-7, NGC 5995, NGC 6552, NGC 7682) are reported. The 12micron S2 sample shows a significantly higher incidence of HBLR (50%) than its CfA counterpart (30%), suggesting that the latter may be incomplete in hidden AGNs. Compared to the non-HBLR S2s, the HBLR S2s display distinctly higher radio power relative to their far-infrared output and hotter dust temperature as indicated by the f25/f60 color. However, the level of obscuration is indistinguishable between the two types of S2. These results strongly support the existence of two intrinsically different populations of S2: one harboring an energetic, hidden S1 nucleus with BLR, and the other, a ``pure S2'', with weak or absent S1 nucleus and a strong, perhaps dominating starburst component. Thus, the simple purely orientation-based unification model is not applicable to all Seyfert galaxies.Comment: 5 pages with embedded figs, ApJ Letters, in pres

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Geometric mutual information at classical critical points

A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior. It is exactly $(c/3)\ln \ell$ for an interval of length $\ell$ in an infinite system, where $c$ is the central charge of the conformal field theory. Here we define the geometric mutual information, an analogous quantity for classical critical points. We compute this for 2d conformal field theories in an arbitrary geometry, and show in particular that for a rectangle cut into two rectangles, it is proportional to $c$. This makes it possible to extract $c$ in classical simulations, which we demonstrate for the critical Ising and 3-state Potts models.Comment: 5 pages. v3: published versio

Detecting Classical Phase Transitions with Renyi Mutual Information

By developing a method to represent the Renyi entropies via a replica-trick on classical statistical mechanical systems, we introduce a procedure to calculate the Renyi Mutual Information in any Monte Carlo simulation. Through simulations on several classical models, we demonstrate that the Renyi Mutual Information can detect finite-temperature critical points, and even identify their universality class, without knowledge of an order parameter or other thermodynamic estimators. Remarkably, in addition to critical points mediated by symmetry breaking, the Renyi Mutual Information is able to detect topological vortex-unbinding transitions, as we explicitly demonstrate on simulations of the XY model.Comment: 5 pages, 4 figure

Jumble Java Byte Code to Measure the Effectiveness of Unit Tests

Jumble is a byte code level mutation testing tool for Java which inter-operates with JUnit. It has been designed to operate in an industrial setting with large projects. Heuristics have been included to speed the checking of mutations, for example, noting which test fails for each mutation and running this first in subsequent mutation checks. Significant effort has been put into ensuring that it can test code which uses custom class loading and reflection. This requires careful attention to class path handling and coexistence with foreign class-loaders. Jumble is currently used on a continuous basis within an agile programming environment with approximately 370,000 lines of Java code under source control. This checks out project code every fifteen minutes and runs an incremental set of unit tests and mutation tests for modified classes. Jumble is being made available as open source