1,033 research outputs found
Entanglement spectra of critical and near-critical systems in one dimension
The entanglement spectrum of a pure state of a bipartite system is the full
set of eigenvalues of the reduced density matrix obtained from tracing out one
part. Such spectra are known in several cases to contain important information
beyond that in the entanglement entropy. This paper studies the entanglement
spectrum for a variety of critical and near-critical quantum lattice models in
one dimension, chiefly by the iTEBD numerical method, which enables both
integrable and non-integrable models to be studied. We find that the
distribution of eigenvalues in the entanglement spectra agrees with an
approximate result derived by Calabrese and Lefevre to an accuracy of a few
percent for all models studied. This result applies whether the correlation
length is intrinsic or generated by the finite matrix size accessible in iTEBD.
For the transverse Ising model, the known exact results for the entanglement
spectrum are used to confirm the validity of the iTEBD approach. For more
general models, no exact result is available but the iTEBD results directly
test the hypothesis that all moments of the reduced density matrix are
determined by a single parameter.Comment: 6 pages, 5 figure
Glassy dynamics and aging in an exactly solvable spin model
We introduce a simple two-dimensional spin model with short-range
interactions which shows glassy behavior despite a Hamiltonian which is
completely homogeneous and possesses no randomness. We solve exactly for both
the static partition function of the model and the distribution of energy
barriers, giving us the equilibration time-scales at low temperature.
Simulations of instantaneous quenches and of annealing of the model are in good
agreement with the analytic calculations. We also measure the two-time spin
correlation as a function of waiting time, and show that the model has aging
behavior consistent with the distribution of barrier heights. The model appears
to have no sharp glass transition. Instead, it falls out of equilibrium at a
temperature which decreases logarithmically as a function of the cooling time.Comment: 16 pages, 4 postscript figures, typeset in LaTeX using the RevTeX
macro packag
Spectral Duality in Integrable Systems from AGT Conjecture
We describe relationships between integrable systems with N degrees of
freedom arising from the AGT conjecture. Namely, we prove the equivalence
(spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N)
Gaudin model both at classical and quantum level. The former one appears on the
gauge theory side of the AGT relation in the Nekrasov-Shatashvili (and further
the Seiberg-Witten) limit while the latter one is natural on the CFT side. At
the classical level, the duality transformation relates the Seiberg-Witten
differentials and spectral curves via a bispectral involution. The quantum
duality extends this to the equivalence of the corresponding Baxter-Schrodinger
equations (quantum spectral curves). This equivalence generalizes both the
spectral self-duality between the 2x2 and NxN representations of the Toda chain
and the famous AHH duality
Some New Results on Complex-Temperature Singularities in Potts Models on the Square Lattice
We report some new results on the complex-temperature (CT) singularities of
-state Potts models on the square lattice. We concentrate on the problematic
region (where ) in which CT zeros of the partition function
are sensitive to finite lattice artifacts. From analyses of low-temperature
series expansions for , we establish the existence, in this
region, of complex-conjugate CT singularities at which the magnetization and
susceptibility diverge. From calculations of zeros of the partition function,
we obtain evidence consistent with the inference that these singularities occur
at endpoints of arcs protruding into the (complex-temperature
extension of the) FM phase. Exponents for these singularities are determined;
e.g., for , we find , consistent with .
By duality, these results also imply associated arcs extending to the (CT
extension of the) symmetric PM phase. Analytic expressions are suggested for
the positions of some of these singularities; e.g., for , our finding is
consistent with the exact value . Further discussions of
complex-temperature phase diagrams are given.Comment: 26 pages, latex, with eight epsf figure
Quantum Liouville theory and BTZ black hole entropy
In this paper I give an explicit conformal field theory description of
(2+1)-dimensional BTZ black hole entropy. In the boundary Liouville field
theory I investigate the reducible Verma modules in the elliptic sector, which
correspond to certain irreducible representations of the quantum algebra
U_q(sl_2) \odot U_{\hat{q}}(sl_2). I show that there are states that decouple
from these reducible Verma modules in a similar fashion to the decoupling of
null states in minimal models. Because ofthe nonstandard form of the Ward
identity for the two-point correlation functions in quantum Liouville field
theory, these decoupling states have positive-definite norms. The explicit
counting from these states gives the desired Bekenstein-Hawking entropy in the
semi-classical limit when q is a root of unity of odd order.Comment: LaTeX, 33 pages, 4 eps figure
Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q
The Q-state Potts model can be extended to noninteger and even complex Q in
the FK representation. In the FK representation the partition function,Z(Q,a),
is a polynomial in Q and v=a-1(a=e^-T) and the coefficients of this
polynomial,Phi(b,c), are the number of graphs on the lattice consisting of b
bonds and c connected clusters. We introduce the random-cluster transfer matrix
to compute Phi exactly on finite square lattices. Given the FK representation
of the partition function we begin by studying the critical Potts model
Z_{CP}=Z(Q,a_c), where a_c=1+sqrt{Q}. We find a set of zeros in the complex
w=sqrt{Q} plane that map to the Beraha numbers for real positive Q. We also
identify tilde{Q}_c(L), the value of Q for a lattice of width L above which the
locus of zeros in the complex p=v/sqrt{Q} plane lies on the unit circle. We
find that 1/tilde{Q}_c->0 as 1/L->0. We then study zeros of the AF Potts model
in the complex Q plane and determine Q_c(a), the largest value of Q for a fixed
value of a below which there is AF order. We find excellent agreement with
Q_c=(1-a)(a+3). We also investigate the locus of zeros of the FM Potts model in
the complex Q plane and confirm that Q_c=(a-1)^2. We show that the edge
singularity in the complex Q plane approaches Q_c as Q_c(L)~Q_c+AL^-y_q, and
determine the scaling exponent y_q. Finally, by finite size scaling of the
Fisher zeros near the AF critical point we determine the thermal exponent y_t
as a function of Q in the range 2<Q<3. We find that y_t is a smooth function of
Q and is well fit by y_t=(1+Au+Bu^2)/(C+Du) where u=u(Q). For Q=3 we find
y_t~0.6; however if we include lattices up to L=12 we find y_t~0.50.Comment: to appear in Physical Review
Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters,
and their complex architectures results in a variety of critical effects
dramatically different from those in cooperative systems on lattices. In the
last few years, researchers have made important steps toward understanding the
qualitatively new critical phenomena in complex networks. We review the
results, concepts, and methods of this rapidly developing field. Here we mostly
consider two closely related classes of these critical phenomena, namely
structural phase transitions in the network architectures and transitions in
cooperative models on networks as substrates. We also discuss systems where a
network and interacting agents on it influence each other. We overview a wide
range of critical phenomena in equilibrium and growing networks including the
birth of the giant connected component, percolation, k-core percolation,
phenomena near epidemic thresholds, condensation transitions, critical
phenomena in spin models placed on networks, synchronization, and
self-organized criticality effects in interacting systems on networks. We also
discuss strong finite size effects in these systems and highlight open problems
and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references,
extende
T-systems and Y-systems in integrable systems
The T and Y-systems are ubiquitous structures in classical and quantum
integrable systems. They are difference equations having a variety of aspects
related to commuting transfer matrices in solvable lattice models, q-characters
of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras
with coefficients, periodicity conjectures of Zamolodchikov and others,
dilogarithm identities in conformal field theory, difference analogue of
L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem,
AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace
sequence in discrete geometry, Fermionic character formulas and combinatorial
completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics,
analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and
so forth. This review article is a collection of short reviews on these topics
which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5,
eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical
review) also needs these correction
Endothelial cells and angiogenesis in the horse in health and disease—A review
The cardiovascular system is the first functional organ in the embryo, and its blood vessels form a widespread conductive network within the organism. Blood vessels develop de novo, by the differentiation of endothelial progenitor cells (vasculogenesis) or by angiogenesis, which is the formation of new blood vessels from existing ones. This review presents an overview of the current knowledge on physiological and pathological angiogenesis in the horse including studies on equine endothelial cells. Principal study fields in equine angiogenesis research were identified: equine endothelial progenitor cells; equine endothelial cells and angiogenesis (heterogeneity, markers and assessment); endothelial regulatory molecules in equine angiogenesis; angiogenesis research in equine reproduction (ovary, uterus, placenta and conceptus, testis); angiogenesis research in pathological conditions (tumours, ocular pathologies, equine wound healing, musculoskeletal system and laminitis). The review also includes a table that summarizes in vitro studies on equine endothelial cells, either describing the isolation procedure or using previously isolated endothelial cells. A particular challenge of the review was that results published are fragmentary and sometimes even contradictory, raising more questions than they answer. In conclusion, angiogenesis is a major factor in several diseases frequently occurring in horses, but relatively few studies focus on angiogenesis in the horse. The challenge for the future is therefore to continue exploring new therapeutic angiogenesis strategies for horses to fill in the missing pieces of the puzzle
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