42 research outputs found
Phase Diagram of a Loop on the Square Lattice
The phase diagram of the O(n) model, in particular the special case , is
studied by means of transfer-matrix calculations on the loop representation of
the O(n) model. The model is defined on the square lattice; the loops are
allowed to collide at the lattice vertices, but not to intersect. The loop
model contains three variable parameters that determine the loop density or
temperature, the energy of a bend in a loop, and the interaction energy of
colliding loop segments. A finite-size analysis of the transfer-matrix results
yields the phase diagram in a special plane of the parameter space. These
results confirm the existence of a multicritical point and an Ising-like
critical line in the low-temperature O(n) phase.Comment: LaTeX, 3 eps file
Emergent O(n) Symmetry in a series of three-dimensional Potts Models
We study the q-state Potts model on the simple cubic lattice with
ferromagnetic interactions in one lattice direction, and antiferromagnetic
interactions in the two other directions. As the temperature T decreases, the
system undergoes a second-order phase transition that fits in the universality
class of the 3D O(n) model with n=q-1. This conclusion is based on the
estimated critical exponents, and histograms of the order parameter. At even
smaller T we find, for q=4 and 5, a first-order transition to a phase with a
different type of long-range order. This long-range order dissolves at T=0, and
the system effectively reduces to a disordered two-dimensional Potts
antiferromagnet. These results are obtained by means of Monte Carlo simulations
and finite-size scaling.Comment: 5 pages, 7 figures, accepted by Physical Review
First and second order transitions in dilute O(n) models
We explore the phase diagram of an O(n) model on the honeycomb lattice with
vacancies, using finite-size scaling and transfer-matrix methods. We make use
of the loop representation of the O(n) model, so that is not restricted to
positive integers. For low activities of the vacancies, we observe critical
points of the known universality class. At high activities the transition
becomes first order. For n=0 the model includes an exactly known theta point,
used to describe a collapsing polymer in two dimensions. When we vary from
0 to 1, we observe a tricritical point which interpolates between the
universality classes of the theta point and the Ising tricritical point.Comment: LaTeX, 6 eps file
Entropy bounds and Cardy-Verlinde formula in Yang-Mills theory
Using gauge formulation of gravity the three-dimensional SU(2) YM theory
equations of motion are presented in equivalent form as FRW cosmological
equations. With the radiation, the particular (periodic, big bang-big crunch)
three-dimensional universe is constructed. Cosmological entropy bounds
(so-called Cardy-Verlinde formula) have the standard form in such universe.
Mapping such universe back to YM formulation we got the thermal solution of YM
theory. The corresponding holographic entropy bounds (Cardy-Verlinde formula)
in YM theory are constructed. This indicates to universal character of
holographic relations.Comment: LaTeX file, 11 pages, a reference is adde
Critical frontier of the triangular antiferromagnet in a field
We study the critical line of the triangular Ising antiferromagnet in an
external magnetic field by means of a finite-size analysis of results obtained
by transfer-matrix and Monte Carlo techniques. We compare the shape of the
critical line with predictions of two different theoretical scenarios. Both
scenarios, while plausible, involve assumptions. The first scenario is based on
the generalization of the model to a vertex model, and the assumption that the
exact analytic form of the critical manifold of this vertex model is determined
by the zeroes of an O(2) gauge-invariant polynomial in the vertex weights.
However, it is not possible to fit the coefficients of such polynomials of
orders up to 10, such as to reproduce the numerical data for the critical
points. The second theoretical prediction is based on the assumption that a
renormalization mapping exists of the Ising model on the Coulomb gas, and
analysis of the resulting renormalization equations. It leads to a shape of the
critical line that is inconsistent with the first prediction, but consistent
with the numerical data.Comment: 13 pages, 9 figure
c-Theorem for Disordered Systems
We find an analog of Zamolodchikov's c-theorem for disordered two dimensional
noninteracting systems in their supersymmetric representation. For this purpose
we introduce a new parameter b which flows along the renormalization group
trajectories much like the central charge for unitary two dimensional field
theories. However, it is not known yet if this flow is irreversible. b turns
out to be related to the central extension of a certain algebra, a
generalization of the Virasoro algebra, which we show may be present at the
critical points of these theories. b is also related to the physical free
energy of the disordered system defined on a cylinder. We discuss possible
applications by computing b for two dimensional Dirac fermions with random
gauge potential.Comment: 7 page
Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
The Casimir problem is usually posed as the response of a fluctuating quantum
field to externally imposed boundary conditions. In reality, however, no
interaction is strong enough to enforce a boundary condition on all frequencies
of a fluctuating field. We construct a more physical model of the situation by
coupling the fluctuating field to a smooth background potential that implements
the boundary condition in a certain limit. To study this problem, we develop
general new methods to compute renormalized one--loop quantum energies and
energy densities. We use analytic properties of scattering data to compute
Green's functions in time--independent background fields at imaginary momenta.
Our calculational method is particularly useful for numerical studies of
singular limits because it avoids terms that oscillate or require cancellation
of exponentially growing and decaying factors. To renormalize, we identify
potentially divergent contributions to the Casimir energy with low orders in
the Born series to the Green's function. We subtract these contributions and
add back the corresponding Feynman diagrams, which we combine with counterterms
fixed by imposing standard renormalization conditions on low--order Green's
functions. The resulting Casimir energy and energy density are finite
functionals for smooth background potentials. In general, however, the Casimir
energy diverges in the boundary condition limit. This divergence is real and
reflects the infinite energy needed to constrain a fluctuating field on all
energy scales; renormalizable quantum field theories have no place for ad hoc
surface counterterms. We apply our methods to simple examples to illustrate
cases where these subtleties invalidate the conclusions of the boundary
condition approach.Comment: 36pages, Latex, 20 eps files. included via epsfi
Boundary Entropy Can Increase Under Bulk RG Flow
The boundary entropy log(g) of a critical one-dimensional quantum system (or
two-dimensional conformal field theory) is known to decrease under
renormalization group (RG) flow of the boundary theory. We study instead the
behavior of the boundary entropy as the bulk theory flows between two nearby
critical points. We use conformal perturbation theory to calculate the change
in g due to a slightly relevant bulk perturbation and find that it has no
preferred sign. The boundary entropy log(g) can therefore increase during
appropriate bulk flows. This is demonstrated explicitly in flows between
minimal models. We discuss the applications of this result to D-branes in
string theory and to impurity problems in condensed matter.Comment: 20 page
On the integrability of two-dimensional models with U(1)xSU(N) symmetry
In this paper we study the integrability of a family of models with
U(1)xSU(N) symmetry. They admit fermionic and bosonic formulations related
through bosonization and subsequent T-duality. The fermionic theory is just the
CP^(N-1) sigma model coupled to a self-interacting massless fermion, while the
bosonic one defines a one-parameter deformation of the O(2N) sigma model. For
N=2 the latter model is equivalent to the integrable deformation of the O(4)
sigma model discovered by Wiegmann. At higher values of N we find that
integrability is more sporadic and requires a fine-tuning of the parameters of
the theory. A special case of our study is the N=4 model, which was found to
describe the AdS_4xCP^3 string theory in the Alday-Maldacena decoupling limit.
In this case we propose a set of asymptotic Bethe ansatz equations for the
energy spectrum.Comment: 61 pages, 7 figure
Entropy from AdS(3)/CFT(2)
We parametrize the (2+1)-dimensional AdS space and the BTZ black hole with
Fefferman-Graham coordinates starting from the AdS boundary. We consider
various boundary metrics: Rindler, static de Sitter and FRW. In each case, we
compute the holographic stress-energy tensor of the dual CFT and confirm that
it has the correct form, including the effects of the conformal anomaly. We
find that the Fefferman-Graham parametrization also spans a second copy of the
AdS space, including a second boundary. For the boundary metrics we consider,
the Fefferman-Graham coordinates do not cover the whole AdS space. We propose
that the length of the line delimiting the excluded region at a given time can
be identified with the entropy of the dual CFT on a background determined by
the boundary metric. For Rindler and de Sitter backgrounds our proposal
reproduces the expected entropy. For a FRW background it produces a
generalization of the Cardy formula that takes into account the vacuum energy
related to the expansion.Comment: major revision with several clarifications and corrections, 22 page