2,295 research outputs found
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 , in , we can define that gives a
new interesting mechanism for breaking scale symmetry in 4-D theories of
gravity plus matter fields, through the equations of
motion which lead to an integration constant the breaks the scale symmetry,
while introducing terms of the form , being the determinant of
the vierbein, being the Gauss Bonnet scalar and being scalar functions
of the fields transforming like (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
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 and
.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
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