Using zeros of the canonical partition function map to detect signatures of a Berezinskii-Kosterlitz-Thouless transition

Using the two dimensional $XY-(S(O(3))$ model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii-Kosterlitz-Thouless ($BKT$) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the $BKT$ class of universality. We obtain $T_{BKT}$ in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions $\mathfrak{Re}(T) \leq T_{BKT}$ and $\mathfrak{Re}(T) > T_{BKT}$ in the thermodynamic limit show that $\mathfrak{Im}(T)$ goes to zero in the former case and is finite in the last one

Periodic Gravitational Waves From Small Cosmic String Loops

We consider a population of small, high-velocity cosmic string loops. We assume the typical length of these loops is determined by the gravitational radiation scale and use the results of \cite{Polchinski:2007rg} which pointed out their highly relativistic nature. A study of the gravitational wave emission from such a population is carried out. The large Lorentz boost involved causes the lowest harmonics of the loops to fall within the frequency band of the LIGO detector. Due to this feature the gravitational waves emitted by such loops can be detected in a periodic search rather than in burst or stochastic analysis. It is shown that, for interesting values of the string tension (10^{-10}\lsim G\mu\lsim 10^{-8}) the detector can observe loops at reasonably high redshifts and that detection is, in principle, possible. We compute the number of expected observations produced by such a process. For a 10 hour search we find that this number is of order $O(10^{-4})$. This is a consequence of the low effective number density of the loops traveling along the line of sight. However, small probabilities of reconnection and longer observation times can improve the result.Comment: 1+15 pages, 7 figure

Electromagnetic Fields of Slowly Rotating Magnetized Gravastars

We study the dipolar magnetic field configuration and present solutions of Maxwell equations in the internal background spacetime of a a slowly rotating gravastar. The shell of gravastar where magnetic field penetrated is modeled as sphere consisting of perfect highly magnetized fluid with infinite conductivity. Dipolar magnetic field of the gravastar is produced by a circular current loop symmetrically placed at radius $a$ at the equatorial plane.Comment: 5 pages, 2 figures, accepted for publication to Mod. Phys. Lett.

Gravitational collapse of Type II fluid in higher dimensional space-times

We find the general solution of the Einstein equation for spherically symmetric collapse of Type II fluid (null strange quark fluid) in higher dimensions. It turns out that the nakedness and curvature strength of the shell focusing singularities carry over to higher dimensions. However, there is shrinkage of the initial data space for a naked singularity of the Vaidya collapse due to the presence of strange quark matter.Comment: RevTex4 style, 4 pages; Accepted in Phys. Rev.

Connecting the Unstable Region of the Entropy to the Pattern of the Fisher's Zeros Map

Phase transitions are one of the most interesting natural phenomena. For finite system, one of the concerns in the topic is how to classify a specific transition as being of first, second, or even of a higher order, according to the Ehrenfest classification. The partition function provides all the thermodynamic information about the physical system, and a phase transition can be identified by the complex temperature where it is equal to zero. In addition, the pattern of the zeros on the complex temperature plan can provide evidences of the order of the transition. In this manuscript, we present an analytical and simulational study connecting the microcanonical analysis of the unstable region of the entropy to the canonical partition function zeros. We show that for the first-order transition the zeros accumulate uniformly in a vertical line on the complex inverse temperature plane as discussed in previous works. We illustrated our calculation using the $147$ particles Lennard-Jones cluster.Comment: 18 pages, 8 figure

Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance

In this article, we study a pseudo-differential inclusion driven by a nonlocal anisotropic operator and a Clarke generalized subdifferential of a nonsmooth potential, which satisfies nonresonance conditions both at the origin and at infinity. We prove the existence of three nontrivial solutions: one positive, one negative and one of unknown sign, using variational methods based on nosmooth critical point theory, more precisely applying the second deformation theorem and spectral theory. Here, a nosmooth anisotropic version of the Hölder versus Sobolev minimizers relation play an important role