Metastates in mean-field models with random external fields generated by Markov chains

We extend the construction by Kuelske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that, for a degenerate non-reversible chain this CLT approximation is not enough and the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.Comment: 20 pages, 2 figure

An ultrametric state space with a dense discrete overlap distribution: Paperfolding sequences

We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding sequences has an ultrametric structure. Our example provides an illustration of some properties which were suggested to occur for pure states in spin glass models

Unified N=2 Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Four Dimensions

We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions. As their defining property, these theories admit the action of a global or local symmetry group that is (i) simple, and (ii) acts irreducibly on all the vector fields of the theory, including the ``graviphoton''. Restricting ourselves to the theories that originate from five dimensions via dimensional reduction, we find that the generic Jordan family of MESGTs with the scalar manifolds [SU(1,1)/U(1)] X [SO(2,n)/SO(2)X SO(n)] are all unified in four dimensions with the unifying global symmetry group SO(2,n). Of these theories only one can be gauged so as to obtain a unified YMESGT with the gauge group SO(2,1). Three of the four magical supergravity theories defined by simple Euclidean Jordan algebras of degree 3 are unified MESGTs in four dimensions. Two of these can furthermore be gauged so as to obtain 4D unified YMESGTs with gauge groups SO(3,2) and SO(6,2), respectively. The generic non-Jordan family and the theories whose scalar manifolds are homogeneous but not symmetric do not lead to unified MESGTs in four dimensions. The three infinite families of unified five-dimensional MESGTs defined by simple Lorentzian Jordan algebras, whose scalar manifolds are non-homogeneous, do not lead directly to unified MESGTs in four dimensions under dimensional reduction. However, since their manifolds are non-homogeneous we are not able to completely rule out the existence of symplectic sections in which these theories become unified in four dimensions.Comment: 47 pages; latex fil

Electroweak Supersymmetry around the Electroweak Scale

Inspired by the phenomenological constraints, LHC supersymmetry and Higgs searches, dark matter search as well as string model building, we propose the electroweak supersymmetry around the electroweak scale: the squarks and/or gluinos are around a few TeV while the sleptons, sneutrinos, bino and winos are within one TeV. The Higgsinos can be either heavy or light. We consider bino as the dominant component of dark matter candidate, and the observed dark matter relic density is achieved via the neutralino-stau coannihilations. Considering the Generalized Minimal Supergravity (GmSUGRA), we show explicitly that the electroweak supersymmetry can be realized, and the gauge coupling unification can be preserved. With two Scenarios, we study the viable parameter spaces that satisfy all the current phenomenological constraints, and we present the concrete benchmark points. Furthermore, we comment on the fine-tuning problem and LHC searches.Comment: RevTex4, 28 pages, 8 figures, 8 tables, version to appear in EPJ

The General Solution of Bianchi Type VIIhVII_h Vacuum Cosmology

The theory of symmetries of systems of coupled, ordinary differential equations (ODE) is used to develop a concise algorithm in order to obtain the entire space of solutions to vacuum Bianchi Einstein Field Equations (EFEs). The symmetries used are the well known automorphisms of the Lie algebra for the corresponding isometry group of each Bianchi Type, as well as the scaling and the time re-parametrization symmetry. The application of the method to Type VII_h results in (a) obtaining the general solution of Type VII_0 with the aid of the third Painlev\'{e} transcendental (b) obtaining the general solution of Type $VII_h$ with the aid of the sixth Painlev\'{e} transcendental (c) the recovery of all known solutions (six in total) without a prior assumption of any extra symmetry (d) The discovery of a new solution (the line element given in closed form) with a G_3 isometry group acting on T_3, i.e. on time-like hyper-surfaces, along with the emergence of the line element describing the flat vacuum Type VII_0 Bianchi Cosmology.Comment: latex2e source file, 27 pages, 2 tables, no fiure

Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields

In this article we study the phase transition phenomenon for the Ising model under the action of a non-uniform external magnetic field. We show that the Ising model on the hypercubic lattice with a summable magnetic field has a first-order phase transition and, for any positive (resp. negative) and bounded magnetic field, the model does not present the phase transition phenomenon whenever $\liminf h_i> 0$, where ${\bf h} = (h_i)_{i \in \Z^d}$ is the external magnetic field.Comment: 11 pages. Published in Journal of Statistical Physics - 201

Special Geometry of Euclidean Supersymmetry I: Vector Multiplets

We construct the general action for Abelian vector multiplets in rigid 4-dimensional Euclidean (instead of Minkowskian) N=2 supersymmetry, i.e., over space-times with a positive definite instead of a Lorentzian metric. The target manifolds for the scalar fields turn out to be para-complex manifolds endowed with a particular kind of special geometry, which we call affine special para-Kahler geometry. We give a precise definition and develop the mathematical theory of such manifolds. The relation to the affine special Kahler manifolds appearing in Minkowskian N=2 supersymmetry is discussed. Starting from the general 5-dimensional vector multiplet action we consider dimensional reduction over time and space in parallel, providing a dictionary between the resulting Euclidean and Minkowskian theories. Then we reanalyze supersymmetry in four dimensions and find that any (para-)holomorphic prepotential defines a supersymmetric Lagrangian, provided that we add a specific four-fermion term, which cannot be obtained by dimensional reduction. We show that the Euclidean action and supersymmetry transformations, when written in terms of para-holomorphic coordinates, take exactly the same form as their Minkowskian counterparts. The appearance of a para-complex and complex structure in the Euclidean and Minkowskian theory, respectively, is traced back to properties of the underlying R-symmetry groups. Finally, we indicate how our work will be extended to other types of multiplets and to supergravity in the future and explain the relevance of this project for the study of instantons, solitons and cosmological solutions in supergravity and M-theory.Comment: 74 page

Light propagation in statistically homogeneous and isotropic universes with general matter content

We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular diameter distance and two typos. No change in result

Resummation of Nonalternating Divergent Perturbative Expansions

A method for the resummation of nonalternating divergent perturbation series is described. The procedure constitutes a generalization of the Borel-Pad\'{e} method. Of crucial importance is a special integration contour in the complex plane. Nonperturbative imaginary contributions can be inferred from the purely real perturbative coefficients. A connection is drawn from the quantum field theoretic problem of resummation to divergent perturbative expansions in other areas of physics.Comment: 5 pages, LaTeX, 2 tables, 1 figure; discussion of the Carleman criterion added; version to appear in Phys. Rev.

Gravitational field around a time-like current-carrying screwed cosmic string in scalar-tensor theories

In this paper we obtain the space-time generated by a time-like current-carrying superconducting screwed cosmic string(TCSCS). This gravitational field is obtained in a modified scalar-tensor theory in the sense that torsion is taken into account. We show that this solution is comptible with a torsion field generated by the scalar field $\phi$. The analysis of gravitational effects of a TCSCS shows up that the torsion effects that appear in the physical frame of Jordan-Fierz can be described in a geometric form given by contorsion term plus a symmetric part which contains the scalar gradient. As an important application of this solution, we consider the linear perturbation method developed by Zel'dovich, investigate the accretion of cold dark matter due to the formation of wakes when a TCSCS moves with speed $v$ and discuss the role played by torsion. Our results are compared with those obtained for cosmic strings in the framework of scalar-tensor theories without taking torsion into account.Comment: 21 pages, no figures, Revised Version, presented at the "XXIV- Encontro Nacional de Fisica de Particulas e Campos ", Caxambu, MG, Brazil, to appear in Phys. Rev.