209 research outputs found
Renormalization group irreversible functions in more than two dimensions
There are two general irreversibility theorems for the renormalization group
in more than two dimensions: the first one is of entropic nature, while the
second one, by Forte and Latorre, relies on the properties of the stress-tensor
trace, and has been recently questioned by Osborn and Shore. We start by
establishing under what assumptions this second theorem can still be valid.
Then it is compared with the entropic theorem and shown to be essentially
equivalent. However, since the irreversible function of the (corrected)
Forte-Latorre theorem is non universal (whereas the relative entropy of the
other theorem is universal), it needs the additional step of renormalization.
On the other hand, the irreversibility theorem is only guaranteed to be
unambiguous if the integral of the stress-tensor trace correlator is finite,
which happens for free theories only in dimension smaller than four.Comment: 4 pages; minor changes to improve readability; to appear in Phys.
Rev.
Angular quantization and the density matrix renormalization group
Path integral techniques for the density matrix of a one-dimensional
statistical system near a boundary previously employed in black-hole physics
are applied to providing a new interpretation of the density matrix
renormalization group: its efficacy is due to the concentration of quantum
states near the boundary.Comment: 8 pages, 3 figures, to appear in Mod. Phys. Lett.
Anisotropy in Homogeneous Rotating Turbulence
The effective stress tensor of a homogeneous turbulent rotating fluid is
anisotropic. This leads us to consider the most general axisymmetric four-rank
``viscosity tensor'' for a Newtonian fluid and the new terms in the turbulent
effective force on large scales that arise from it, in addition to the
microscopic viscous force. Some of these terms involve couplings to vorticity
and others are angular momentum non conserving (in the rotating frame).
Furthermore, we explore the constraints on the response function and the
two-point velocity correlation due to axisymmetry. Finally, we compare our
viscosity tensor with other four-rank tensors defined in current approaches to
non-rotating anisotropic turbulence.Comment: 14 pages, RevTe
Statistics and geometry of cosmic voids
We introduce new statistical methods for the study of cosmic voids, focusing
on the statistics of largest size voids. We distinguish three different types
of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like
distributions. The last two distributions are connected with two types of
fractal geometry of the matter distribution. Scaling voids with Pareto
distribution appear in fractal distributions with box-counting dimension
smaller than three (its maximum value), whereas the lognormal void distribution
corresponds to multifractals with box-counting dimension equal to three.
Moreover, voids of the former type persist in the continuum limit, namely, as
the number density of observable objects grows, giving rise to lacunar
fractals, whereas voids of the latter type disappear in the continuum limit,
giving rise to non-lacunar (multi)fractals. We propose both lacunar and
non-lacunar multifractal models of the cosmic web structure of the Universe. A
non-lacunar multifractal model is supported by current galaxy surveys as well
as cosmological -body simulations. This model suggests, in particular, that
small dark matter halos and, arguably, faint galaxies are present in cosmic
voids.Comment: 39 pages, 8 EPS figures, supersedes arXiv:0802.038
Stochastic formulation of the renormalization group: supersymmetric structure and topology of the space of couplings
The exact or Wilson renormalization group equations can be formulated as a
functional Fokker-Planck equation in the infinite-dimensional configuration
space of a field theory, suggesting a stochastic process in the space of
couplings. Indeed, the ordinary renormalization group differential equations
can be supplemented with noise, making them into stochastic Langevin equations.
Furthermore, if the renormalization group is a gradient flow, the space of
couplings can be endowed with a supersymmetric structure a la Parisi-Sourlas.
The formulation of the renormalization group as supersymmetric quantum
mechanics is useful for analysing the topology of the space of couplings by
means of Morse theory. We present simple examples with one or two couplings.Comment: 13 pages, based on contribution to "Progress in Supersymmetric
Quantum Mechanics" (Valladolid U.), accepted in Journal of Physics
Analysis of a three-component model phase diagram by Catastrophe Theory: Potentials with two Order Parameters
In this work we classify the singularities obtained from the Gibbs potential
of a lattice gas model with three components, two order parameters and five
control parameters applying the general theorems provided by Catastrophe
Theory. In particular, we clearly establish the existence of Landau potentials
in two variables or, in other words, corank 2 canonical forms that are
associated to the hyperbolic umbilic, D_{+4}, its dual the elliptic umbilic,
D_{-4}, and the parabolic umbilic, D_5, catastrophes. The transversality of the
potential with two order parameters is explicitely shown for each case. Thus we
complete the Catastrophe Theory analysis of the three-component lattice model,
initiated in a previous paper.Comment: 17 pages, 3 EPS figures, Latex file, continuation of Phys. Rev. B57,
13527 (1998) (cond-mat/9707015), submitted to Phys. Rev.
Relative entropy for compact Riemann surfaces
The relative entropy of the massive free bosonic field theory is studied on
various compact Riemann surfaces as a universal quantity with physical
significance, in particular, for gravitational phenomena. The exact expression
for the sphere is obtained, as well as its asymptotic series for large mass and
its Taylor series for small mass. One can also derive exact expressions for the
torus but not for higher genus. However, the asymptotic behaviour for large
mass can always be established-up to a constant-with heat-kernel methods. It
consists of an asymptotic series determined only by the curvature, hence common
for homogeneous surfaces of genus higher than one, and exponentially vanishing
corrections whose form is determined by the concrete topology. The coefficient
of the logarithmic term in this series gives the conformal anomaly.Comment: 20 pages, LaTeX 2e, 2 PS figures; to appear in Phys. Rev.
Relative entropy in 2d Quantum Field Theory, finite-size corrections and irreversibility of the Renormalization Group
The relative entropy in two-dimensional Field Theory is studied for its
application as an irreversible quantity under the Renormalization Group,
relying on a general monotonicity theorem for that quantity previously
established. In the cylinder geometry, interpreted as finite-temperature field
theory, one can define from the relative entropy a monotonic quantity similar
to Zamolodchikov's c function. On the other hand, the one-dimensional quantum
thermodynamic entropy also leads to a monotonic quantity, with different
properties. The relation of thermodynamic quantities with the complex
components of the stress tensor is also established and hence the entropic c
theorems are proposed as analogues of Zamolodchikov's c theorem for the
cylinder geometry.Comment: 5 pages, Latex file, revtex, reorganized to best show the generality
of the results, version to appear in Phys. Rev. Let
Entropic C-theorems in free and interacting two-dimensional field theories
The relative entropy in two-dimensional field theory is studied on a cylinder
geometry, interpreted as finite-temperature field theory. The width of the
cylinder provides an infrared scale that allows us to define a dimensionless
relative entropy analogous to Zamolodchikov's function. The one-dimensional
quantum thermodynamic entropy gives rise to another monotonic dimensionless
quantity. I illustrate these monotonicity theorems with examples ranging from
free field theories to interacting models soluble with the thermodynamic Bethe
ansatz. Both dimensionless entropies are explicitly shown to be monotonic in
the examples that we analyze.Comment: 34 pages, 3 figures (8 EPS files), Latex2e file, continuation of
hep-th/9710241; rigorous analysis of sufficient conditions for universality
of the dimensionless relative entropy, more detailed discussion of the
relation with Zamolodchikov's theorem, references added; to appear in Phys.
Rev.
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