14 research outputs found
Multicritical microscopic spectral correlators of hermitian and complex matrices
We find the microscopic spectral densities and the spectral correlators associated with multicritical
behavior for both hermitian and complex matrix ensembles, and show their universality.
We conjecture that microscopic spectral densities of Dirac operators in certain theories without
spontaneous chiral symmetry breaking may belong to these new universality classes
Critical statistics in a power-law random banded matrix ensemble
We investigate the statistical properties of the eigenvalues and eigenvectors
in a random matrix ensemble with . It is known that
this model shows a localization-delocalization transition (LDT) as a function
of the parameter . The model is critical at and the eigenstates
are multifractals. Based on numerical simulations we demonstrate that the
spectral statistics at criticality differs from semi-Poisson statistics which
is expected to be a general feature of systems exhibiting a LDT or `weak
chaos'.Comment: 4 pages in PS including 5 figure
Low-energy couplings of QCD from current correlators near the chiral limit
We investigate a new numerical procedure to compute fermionic correlation
functions at very small quark masses. Large statistical fluctuations, due to
the presence of local ``bumps'' in the wave functions associated with the
low-lying eigenmodes of the Dirac operator, are reduced by an exact low-mode
averaging. To demonstrate the feasibility of the technique, we compute the
two-point correlator of the left-handed vector current with Neuberger fermions
in the quenched approximation, for lattices with a linear extent of L~1.5 fm, a
lattice spacing a~0.09 fm, and quark masses down to the epsilon-regime. By
matching the results with the corresponding (quenched) chiral perturbation
theory expressions, an estimate of (quenched) low-energy constants can be
obtained. We find agreement between the quenched values of F extrapolated from
the p-regime and extracted in the epsilon-regime.Comment: 20 pages, 5 figure
Low-energy couplings of QCD from topological zero-mode wave functions
By matching 1/m^2 divergences in finite-volume two-point correlation
functions of the scalar or pseudoscalar densities with those obtained in chiral
perturbation theory, we derive a relation between the Dirac operator zero-mode
eigenfunctions at fixed non-trivial topology and the low-energy constants of
QCD. We investigate the feasibility of using this relation to extract the pion
decay constant, by computing the zero-mode correlation functions on the lattice
in the quenched approximation and comparing them with the corresponding
expressions in quenched chiral perturbation theory.Comment: 31 pages. v2: references and a small clarification added; published
versio
Spectral Properties of the Overlap Dirac Operator in QCD
We discuss the eigenvalue distribution of the overlap Dirac operator in
quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and
\beta = 6. We distinguish the topological sectors and study the distributions
of the leading non-zero eigenvalues, which are stereographically mapped onto
the imaginary axis. Thus they can be compared to the predictions of random
matrix theory applied to the \epsilon-expansion of chiral perturbation theory.
We find a satisfactory agreement, if the physical volume exceeds about (1.2
fm)^{4}. For the unfolded level spacing distribution we find an accurate
agreement with the random matrix conjecture on all volumes that we considered.Comment: 16 pages, 8 figures, final version published in JHE
Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem
In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95, 230201 (2005)], an exact solution was reported for the probability p_{n,k} to find exactly k real eigenvalues in the spectrum of an nxn real asymmetric matrix drawn at
random from Ginibre's Orthogonal Ensemble (GinOE). In the present paper, we offer a detailed derivation of the above result by concentrating on the proof of the Pfaffian integration theorem, the
key ingredient of our analysis of the statistics of real eigenvalues in the GinOE. We also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a
GinOE matrix restricted to have exactly k real eigenvalues. In the particular case of k=0, all correlation functions of complex eigenvalues are determined
Massive chiral random matrix ensembles at beta = 1 & 4 : Finite-volume QCD partition functions
In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and
real quarks are described by chiral orthogonal and symplectic ensembles of
random matrices. Using this correspondence, general expressions for the QCD
partition functions are derived in terms of microscopically rescaled mass
variables. In limited cases, correlation functions of Dirac eigenvalues and
distributions of the smallest Dirac eigenvalue are given as ratios of these
partition functions. When all masses are degenerate, our results reproduce the
known expressions for the partition functions of zero-dimensional sigma models.Comment: 6 pages, REVTeX 3.1, no figure; (v2) corrected signatures of c'
Axial Correlation Functions in the epsilon-Regime: a Numerical Study with Overlap Fermions
We present simulation results employing overlap fermions for the axial
correlation functions in the epsilon-regime of chiral perturbation theory. In
this regime, finite size effects and topology play a dominant role. Their
description by quenched chiral perturbation theory is compared to our numerical
results in quenched QCD. We show that lattices with a linear extent L > 1.1 fm
are necessary to interpret the numerical data obtained in distinct topological
sectors in terms of the epsilon-expansion. Such lattices are, however, still
substantially smaller than the ones needed in standard chiral perturbation
theory. However, we also observe severe difficulties at very low values of the
quark mass, in particular in the topologically trivial sector.Comment: 15 pages, 6 figures, final version published in JHE
Lattice QCD in the epsilon-regime and random matrix theory
In the epsilon-regime of QCD the main features of the spectrum of the
low-lying eigenvalues of the (euclidean) Dirac operator are expected to be
described by a certain universality class of random matrix models. In
particular, the latter predict the joint statistical distribution of the
individual eigenvalues in any topological sector of the theory. We compare some
of these predictions with high-precision numerical data obtained from lattice
QCD for a range of lattice spacings and volumes. While no complete matching is
observed, the results agree with theoretical expectations at volumes larger
than about 5 fm^4.Comment: Plain TeX source, 17 pages, figures included, minor changes in tables
3 and