10,101 research outputs found

### Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can
be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an
overview of field-theoretical results obtained from the analysis of high-order
perturbative series in the frameworks of the $\epsilon$ and of the
fixed-dimension d=3 expansions. In particular, we discuss the stability of the
O(N)-symmetric fixed point in a generic N-component theory, the critical
behaviors of randomly dilute Ising-like systems and frustrated spin systems
with noncollinear order, the multicritical behavior arising from the
competition of two distinct types of ordering with symmetry O($n_1$) and
O($n_2$) respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200

### Dynamic crossover in the global persistence at criticality

We investigate the global persistence properties of critical systems relaxing
from an initial state with non-vanishing value of the order parameter (e.g.,
the magnetization in the Ising model). The persistence probability of the
global order parameter displays two consecutive regimes in which it decays
algebraically in time with two distinct universal exponents. The associated
crossover is controlled by the initial value m_0 of the order parameter and the
typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo
simulations of the two-dimensional Ising model with Glauber dynamics display
clearly this crossover. The measured exponent of the ultimate algebraic decay
is in rather good agreement with our theoretical predictions for the Ising
universality class.Comment: 5 pages, 2 figure

### Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations

Many alternative formulations of Einstein's evolution have lately been
examined, in an effort to discover one which yields slow growth of
constraint-violating errors. In this paper, rather than directly search for
well-behaved formulations, we instead develop analytic tools to discover which
formulations are particularly ill-behaved. Specifically, we examine the growth
of approximate (geometric-optics) solutions, studied only in the future domain
of dependence of the initial data slice (e.g. we study transients). By
evaluating the amplification of transients a given formulation will produce, we
may therefore eliminate from consideration the most pathological formulations
(e.g. those with numerically-unacceptable amplification). This technique has
the potential to provide surprisingly tight constraints on the set of
formulations one can safely apply. To illustrate the application of these
techniques to practical examples, we apply our technique to the 2-parameter
family of evolution equations proposed by Kidder, Scheel, and Teukolsky,
focusing in particular on flat space (in Rindler coordinates) and Schwarzchild
(in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.

### Experimental study of vapor-cell magneto-optical traps for efficient trapping of radioactive atoms

We have studied magneto-optical traps (MOTs) for efficient on-line trapping
of radioactive atoms. After discussing a model of the trapping process in a
vapor cell and its efficiency, we present the results of detailed experimental
studies on Rb MOTs. Three spherical cells of different sizes were used. These
cells can be easily replaced, while keeping the rest of the apparatus
unchanged: atomic sources, vacuum conditions, magnetic field gradients, sizes
and power of the laser beams, detection system. By direct comparison, we find
that the trapping efficiency only weakly depends on the MOT cell size. It is
also found that the trapping efficiency of the MOT with the smallest cell,
whose diameter is equal to the diameter of the trapping beams, is about 40%
smaller than the efficiency of larger cells. Furthermore, we also demonstrate
the importance of two factors: a long coated tube at the entrance of the MOT
cell, used instead of a diaphragm; and the passivation with an alkali vapor of
the coating on the cell walls, in order to minimize the losses of trappable
atoms. These results guided us in the construction of an efficient
large-diameter cell, which has been successfully employed for on-line trapping
of Fr isotopes at INFN's national laboratories in Legnaro, Italy.Comment: 9 pages, 7 figures, submitted to Eur. Phys. J.

### Simulation of time evolution with the MERA

We describe an algorithm to simulate time evolution using the Multi-scale
Entanglement Renormalization Ansatz (MERA) and test it by studying a critical
Ising chain with periodic boundary conditions and with up to L ~ 10^6 quantum
spins. The cost of a simulation, which scales as L log(L), is reduced to log(L)
when the system is invariant under translations. By simulating an evolution in
imaginary time, we compute the ground state of the system. The errors in the
ground state energy display no evident dependence on the system size. The
algorithm can be extended to lattice systems in higher spatial dimensions.Comment: final version with data improvement (precision and size), 4.1 pages,
4 figures + extra on X

### Entanglement entropy of two disjoint intervals in c=1 theories

We study the scaling of the Renyi entanglement entropy of two disjoint blocks
of critical lattice models described by conformal field theories with central
charge c=1. We provide the analytic conformal field theory result for the
second order Renyi entropy for a free boson compactified on an orbifold
describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual
line. We have checked this prediction in cluster Monte Carlo simulations of the
classical two dimensional AT model. We have also performed extensive numerical
simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor
network techniques that allowed to obtain the reduced density matrices of
disjoint blocks of the spin-chain and to check the correctness of the
predictions for Renyi and entanglement entropies from conformal field theory.
In order to match these predictions, we have extrapolated the numerical results
by properly taking into account the corrections induced by the finite length of
the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure

### Universal parity effects in the entanglement entropy of XX chains with open boundary conditions

We consider the Renyi entanglement entropies in the one-dimensional XX
spin-chains with open boundary conditions in the presence of a magnetic field.
In the case of a semi-infinite system and a block starting from the boundary,
we derive rigorously the asymptotic behavior for large block sizes on the basis
of a recent mathematical theorem for the determinant of Toeplitz plus Hankel
matrices. We conjecture a generalized Fisher-Hartwig form for the corrections
to the asymptotic behavior of this determinant that allows the exact
characterization of the corrections to the scaling at order o(1/l) for any n.
By combining these results with conformal field theory arguments, we derive
exact expressions also in finite chains with open boundary conditions and in
the case when the block is detached from the boundary.Comment: 24 pages, 9 figure

### Correlation amplitude and entanglement entropy in random spin chains

Using strong-disorder renormalization group, numerical exact diagonalization,
and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ
spin-1/2 chain focusing on the long-length and ground-state behavior of the
average time-independent spin-spin correlation function C(l)=\upsilon
l^{-\eta}. In addition to the well-known universal (disorder-independent)
power-law exponent \eta=2, we find interesting universal features displayed by
the prefactor \upsilon=\upsilon_o/3, if l is odd, and \upsilon=\upsilon_e/3,
otherwise. Although \upsilon_o and \upsilon_e are nonuniversal (disorder
dependent) and distinct in magnitude, the combination \upsilon_o + \upsilon_e =
-1/4 is universal if C is computed along the symmetric (longitudinal) axis. The
origin of the nonuniversalities of the prefactors is discussed in the
renormalization-group framework where a solvable toy model is considered.
Moreover, we relate the average correlation function with the average
entanglement entropy, whose amplitude has been recently shown to be universal.
The nonuniversalities of the prefactors are shown to contribute only to surface
terms of the entropy. Finally, we discuss the experimental relevance of our
results by computing the structure factor whose scaling properties,
interestingly, depend on the correlation prefactors.Comment: v1: 16 pages, 15 figures; v2: 17 pages, improved discussions and
statistics, references added, published versio

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