Markov chain sampling of the O(n)O(n) loop models on the infinite plane

It was recently proposed in https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.043322 [Herdeiro & Doyon Phys.,Rev.,E (2016)] a numerical method showing a precise sampling of the infinite plane 2d critical Ising model for finite lattice subsections. The present note extends the method to a larger class of models, namely the $O(n)$ loop gas models for $n \in (1,2]$. We argue that even though the Gibbs measure is non local, it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored. Our results attempt to show that provided an efficient Markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the $O(n)$ models can be numerically studied with efficiency similar to the Ising case. This confirms that scale invariance is the only requirement for the present numerical method to work.Comment: v2: added conclusion section, changes in introduction and appendice

Non-linearities in the quantum multiverse

It has been recently proposed that the multiverse of eternal inflation and the many-worlds interpretation of quantum mechanics can be identified, yielding a new view on the measure and measurement problems. In the present note, we argue that a non-linear evolution of observables in the quantum multiverse would be an obstacle for such a description and that these non-linearities are expected from quite general arguments.Comment: 7 page

A Monte Carlo method for critical systems in infinite volume: the planar Ising model

In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated to generating critical distributions on finite lattices. It uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of "holographic" boundary condition that encodes the presence of an infinite volume beyond it. We check the quality of the distribution obtained in the case of the planar Ising model by comparing various observables with their infinite-plane prediction. We accurately reproduce planar two-, three- and four-point functions of spin and energy operators. We also define a lattice stress-energy tensor, and numerically obtain the associated conformal Ward identities and the Ising central charge.Comment: 43 pages, 21 figure

Non-linear Q-clouds around Kerr black holes

Q-balls are regular extended `objects' that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces - existence lines - of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.Comment: 11 pages, 4 figure

On the interaction between two Kerr black holes

The double-Kerr solution is generated using both a Backlund transformation and the Belinskii-Zakharov inverse-scattering technique. We build a dictionary between the parametrisations naturally obtained in the two methods and show their equivalence. We then focus on the asymptotically flat double-Kerr system obeying the axis condition which is Z_2^\phi invariant; for this system there is an exact formula for the force between the two black holes, in terms of their physical quantities and the coordinate distance. We then show that 1) the angular velocity of the two black holes decreases from the usual Kerr value at infinite distance to zero in the touching limit; 2) the extremal limit of the two black holes is given by |J|=cM^2, where c depends on the distance and varies from one to infinity as the distance decreases; 3) for sufficiently large angular momentum the temperature of the black holes attains a maximum at a certain finite coordinate distance. All of these results are interpreted in terms of the dragging effects of the system.Comment: 19 pages, 4 figures. v2: changed statement about thermodynamical equilibrium in section 3; minor changes; added references. v3: added references to previous relevant work; removed one equation (see note added); other minor corrections; final version to be published in JHE

n-DBI gravity

n-DBI gravity is a gravitational theory introduced in arXiv:1109.1468 [hep-th], motivated by Dirac-Born-Infeld type conformal scalar theory and designed to yield non-eternal inflation spontaneously. It contains a foliation structure provided by an everywhere time-like vector field n, which couples to the gravitational sector of the theory, but decouples in the small curvature limit. We show that any solution of Einstein gravity with a particular curvature property is a solution of n-DBI gravity. Amongst them is a class of geometries isometric to Reissner-Nordstrom-(Anti) de Sitter black hole, which is obtained within the spherically symmetric solutions of n-DBI gravity minimally coupled to the Maxwell field. These solutions have, however, two distinct features from their Einstein gravity counterparts: 1) the cosmological constant appears as an integration constant and can be positive, negative or vanishing, making it a variable quantity of the theory; 2) there is a non-uniqueness of solutions with the same total mass, charge and effective cosmological constant. Such inequivalent solutions cannot be mapped to each other by a foliation preserving diffeomorphism. Physically they are distinguished by the expansion and shear of the congruence tangent to n, which define scalar invariants on each leave of the foliation.Comment: 13 page