Einstein-Yang-Mills-Chern-Simons solutions in D=2n+1 dimensions

We investigate finite energy solutions of the Einstein--Yang-Mills--Chern-Simons system in odd spacetime dimensions, D=2n+1, with n>1. Our configurations are static and spherically symmetric, approaching at infinity a Minkowski spacetime background. In contrast with the Abelian case, the contribution of the Chern-Simons term is nontrivial already in the static, spherically symmetric limit. Both globally regular, particle-like solutions and black holes are constructed numerically for several values of D. These solutions carry a nonzero electric charge and have finite mass. For globally regular solutions, the value of the electric charge is fixed by the Chern-Simons coupling constant. The black holes can be thought as non-linear superpositions of Reissner-Nordstrom and non-Abelian configurations. A systematic discussion of the solutions is given for D=5, in which case the Reissner-Nordstrom black hole becomes unstable and develops non-Abelian hair. We show that some of these non-Abelian configurations are stable under linear, spherically symmetric perturbations. A detailed discussion of an exact D=5 solution describing extremal black holes and solitons is also provided.Comment: 34 pages, 14 figures; v2: misprints corrected and references adde

On d=4d=4 Yang-Mills instantons in a spherically symmetric background

We present arguments for the existence of self-dual Yang-Mills instantons for several spherically symmetric backgrounds with Euclidean signature. The time-independent Yang-Mills field has finite action and a vanishing energy momentum tensor and does not disturb the geometry. We conjecture the existence of similar solutions for any nonextremal SO(3)-spherically symmetric background.Comment: 6 pages, 3 figures; v2: references adde

Thermodynamic behavior of the XXZ Heisenberg s=1/2 chain around the factorizing magnetic field

We have investigated the zero and finite temperature behaviors of the anisotropic antiferromagnetic Heisenberg XXZ spin-1/2 chain in the presence of a transverse magnetic field (h). The attention is concentrated on an interval of magnetic field between the factorizing field (h_f) and the critical one (h_c). The model presents a spin-flop phase for 0<h<h_f with an energy scale which is defined by the long range antiferromagnetic order while it undergoes an entanglement phase transition at h=h_f. The entanglement estimators clearly show that the entanglement is lost exactly at h=h_f which justifies different quantum correlations on both sides of the factorizing field. As a consequence of zero entanglement (at h=h_f) the ground state is known exactly as a product of single particle states which is the starting point for initiating a spin wave theory. The linear spin wave theory is implemented to obtain the specific heat and thermal entanglement of the model in the interested region. A double peak structure is found in the specific heat around h=h_f which manifests the existence of two energy scales in the system as a result of two competing orders before the critical point. These results are confirmed by the low temperature Lanczos data which we have computed.Comment: Will be published in JPCM (2010), 7 figure

Exact sampling for intractable probability distributions via a Bernoulli factory

Many applications in the field of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging. A desire to overcome these problems has led to the development of exact, or perfect, sampling algorithms which convert a Markov chain into an algorithm that produces i.i.d. samples from the stationary distribution. Unfortunately, very few of these algorithms have been developed for the distributions that arise in statistical applications, which typically have uncountable support. Here we study an exact sampling algorithm using a geometrically ergodic Markov chain on a general state space. Our work provides a significant reduction to the number of input draws necessary for the Bernoulli factory, which enables exact sampling via a rejection sampling approach. We illustrate the algorithm on a univariate Metropolis-Hastings sampler and a bivariate Gibbs sampler, which provide a proof of concept and insight into hyper-parameter selection. Finally, we illustrate the algorithm on a Bayesian version of the one-way random effects model with data from a styrene exposure study.Comment: 28 pages, 2 figure