Critical Point of a Symmetric Vertex Model

We study a symmetric vertex model, that allows 10 vertex configurations, by use of the corner transfer matrix renormalization group (CTMRG), a variant of DMRG. The model has a critical point that belongs to the Ising universality class.Comment: 2 pages, 6 figures, short not

Scale Symmetry Breaking From Total Derivative Densities and the Cosmological Constant Problem

The use in the action integral of totally divergent densities in generally coordinate invariant theories can lead to interesting mechanisms of spontaneous symmetry breaking of scale invariance. With dependence in the action on a metric independent density $\Phi$, in $4D$ , we can define $\Phi =\varepsilon^{\mu\nu\alpha\beta}\partial_{\mu}A_{\nu\alpha\beta}$ that gives a new interesting mechanism for breaking scale symmetry in 4-D theories of gravity plus matter fields, through the $A_{\nu\alpha\beta}$ equations of motion which lead to an integration constant the breaks the scale symmetry, while introducing terms of the form $eG ln K$ , $e$ being the determinant of the vierbein, $G$ being the Gauss Bonnet scalar and $K$ being scalar functions of the fields transforming like $K \rightarrow cK$ (where c is a constant) under a scale transformation. Such a term is invariant only up to a total divergence and therefore leads to breaking of scale invariance due to gravitational instantons. The topological density constructed out of gauge field strengths $\varepsilon^{\mu\nu\alpha\beta}F^a_{\mu\nu}F^a_{\alpha\beta}$ can be coupled to the dilaton field linearly to produce a scale invariant term up to a total divergence. The scale symmetry can be broken by Yang Mills instantons which lead to a very small vacuum energy for our Universe.Comment: Accepted for Publication in Physics Letters B, 15 page

Phase Diagram of a 2D Vertex Model

Phase diagram of a symmetric vertex model which allows 7 vertex configurations is obtained by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The critical indices of this model are identified as $\beta = 1/8$ and $\alpha = 0$.Comment: 2 pages, 5 figures, short not

Two-Time Physics with gravitational and gauge field backgrounds

It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d-dimensions (one-time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained by generalizing the worldline formulation of two-time physics by including background fields. A given two-time model, with a fixed set of background fields, can be gauged fixed from d+2 dimensions to (d-1) +1 dimensions to produce diverse one-time dynamical models, all of which are dually related to each other under the underlying gauge symmetry of the unified two-time theory. To satisfy the gauge symmetry of the two-time theory the background fields must obey certain coupled differential equations that are generally covariant and gauge invariant in the target d+2 dimensional spacetime. The gravitational background obeys a null homothety condition while the gauge field obeys a differential equation that generalizes a similar equation derived by Dirac in 1936. Explicit solutions to these coupled equations show that the usual gravitational, gauge, and other interactions in d dimensions may be viewed as embedded in the higher d+2 dimensional space, thus displaying higher spacetime symmetries that otherwise remain hidden.Comment: Latex, 19 pages, references adde

Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group

We report a way of obtaining a spin configuration snapshot, which is one of the representative spin configurations in canonical ensemble, in a finite area of infinite size two-dimensional (2D) classical lattice models. The corner transfer matrix renormalization group (CTMRG), a variant of the density matrix renormalization group (DMRG), is used for the numerical calculation. The matrix product structure of the variational state in CTMRG makes it possible to stochastically fix spins each by each according to the conditional probability with respect to its environment.Comment: 4 pages, 8figure

Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane

Critical behavior of the Ising model is investigated at the center of large scale finite size systems, where the lattice is represented as the tiling of pentagons. The system is on the hyperbolic plane, and the recursive structure of the lattice makes it possible to apply the corner transfer matrix renormalization group method. From the calculated nearest neighbor spin correlation function and the spontaneous magnetization, it is concluded that the phase transition of this model is mean-field like. One parameter deformation of the corner Hamiltonian on the hyperbolic plane is discussed.Comment: 4 pages, 5 figure

Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models

We develop a new variant of the recently introduced stochastic transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process, are studied and compared to exact data and Monte-Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10^5 shows a considerable improvement to the old stochastic TMRG algorithm.Comment: 15 pages, uses IOP styl

Conformal Symmetry and Duality between Free Particle, H-atom and Harmonic Oscillator

We establish a duality between the free massless relativistic particle in d dimensions, the non-relativistic hydrogen atom (1/r potential) in (d-1) space dimensions, and the harmonic oscillator in (d-2) space dimensions with its mass given as the lightcone momentum of an additional dimension. The duality is in the sense that the classical action of these systems are gauge fixed forms of the same worldline gauge theory action at the classical level, and they are all described by the same unitary representation of the conformal group SO(d,2) at the quantum level. The worldline action has a gauge symmetry Sp(2) which treats canonical variables (x,p) as doublets and exists only with a target spacetime that has d spacelike dimensions and two timelike dimensions. This spacetime is constrained due to the gauge symmetry, and the various dual solutions correspond to solutions of the constraints with different topologies. For example, for the H-atom the two timelike dimensions X^{0'},X^{0} live on a circle. The model provides an example of how realistic physics can be viewed as existing in a larger covariant space that includes two timelike coordinates, and how the covariance in the larger space unifies different looking physics into a single system.Comment: Latex, 23 pages, minor improvements. In v3 a better gauge choice for u for the H-atom is made; the results are the sam

Gauge symmetry in phase space with spin, a basis for conformal symmetry and duality among many interactions

We show that a simple OSp(1/2) worldline gauge theory in 0-brane phase space (X,P), with spin degrees of freedom, formulated for a d+2 dimensional spacetime with two times X^0,, X^0', unifies many physical systems which ordinarily are described by a 1-time formulation. Different systems of 1-time physics emerge by choosing gauges that embed ordinary time in d+2 dimensions in different ways. The embeddings have different topology and geometry for the choice of time among the d+2 dimensions. Thus, 2-time physics unifies an infinite number of 1-time physical interacting systems, and establishes a kind of duality among them. One manifestation of the two times is that all of these physical systems have the same quantum Hilbert space in the form of a unique representation of SO(d,2) with the same Casimir eigenvalues. By changing the number n of spinning degrees of freedom the gauge group changes to OSp(n/2). Then the eigenvalue of the Casimirs of SO(d,2) depend on n and then the content of the 1-time physical systems that are unified in the same representation depend on n. The models we study raise new questions about the nature of spacetime.Comment: Latex, 42 pages. v2 improvements in AdS section. In v3 sec.6.2 is modified; the more general potential is limited to a smaller clas