Related papers: Randomness on the Lattice
We calculate the partition function of partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order using the supersymmetry method in the formulation without a singlet particle. We include a nonzero imaginary…
A unified classification and analysis is presented of two dimensional Dirac operators of QCD-like theories in the continuum as well as in a naive lattice discretization. Thereby we consider the quenched theory in the strong coupling limit.…
We investigate the Dirac eigenvalue spectrum ($\rho(\lambda,m_l)$) to study the microscopic origin of axial anomaly in high temperature phase of QCD. We propose novel relations between the derivatives ($\partial^n \rho(\lambda,m_l)/\partial…
We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) and U(1) gauge theory as well as in full QCD with two colors and finite chemical potential. Along the strong-coupling axis up to the phase transition, the…
An important tool for the analysis of results of numerical simulations of lattice QCD is chiral perturbation theory. In Wilson chiral perturbation theory the effects of the finite lattice spacing $a$ are taken into account. In recent years…
We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac…
We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD on a $6^3\times 4$ lattice. As a measure of the fluctuation properties of the eigenvalues, we study the nearest-neighbor spacing…
In the epsilon-regime of lattice QCD one can get an accurate measurement of the pion decay constant F_pi by monitoring how just one single Dirac operator eigenvalue splits into two when subjected to two different external vector sources.…
As a non-perturbative and gauge invariant regularization the lattice provides a tool for deeper understanding of the celebrated Yang-Mills theory, QCD and chiral gauge theories. For illustration, I discuss some analytic developments on the…
We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories…
In this lecture we discuss various aspects of QCD at nonzero chemical potential, including its phase diagram and the Dirac spectrum, and summarize what chiral random matrix theory has contributed to this subject. To illustrate the…
The correlations of the QCD Dirac eigenvalues are studied with use of an extended chiral random matrix model. The inclusion of spatial dependence which the original model lacks enables us to investigate the effects of diffusion modes. We…
Chiral perturbation theory gives direct and unambiguous predictions for the form of various two-point hadronic correlators at low momentum in terms of a finite set of couplings in a chiral Lagrangian. In this paper we study the feasibility…
We calculate numerically the eigenvalue distribution of the overlap Dirac operator in the quenched Schwinger model on a lattice. The distribution does not fit any of the three universality classes of spontaneous chiral symmetry breaking,…
The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS) via the Banks-Casher relation. At the same time the distribution of the near-zero modes is well described by the Random Matrix…
We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-colour lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues…
We evaluate level spacing and smallest eigenvalue distributions of chiral random matrix ensembles transiting from symplectic or orthogonal to unitary symmetry classes with a crossover parameter rho. As expected from the effective sigma…
At low temperature the low-lying QCD Dirac spectrum obeys random matrix statistics. Recently we found that above $T_{c}$ the lowest part of the spectrum consists of localized modes that obey Poisson statistics. An interesting implication of…
A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with non-vanishing chemical potential. We derive new matrix model correlation functions which predict the local fluctuations of complex Dirac…
In the last few years, the supersymmetry method was generalized to real-symmetric, Hermitean, and Hermitean self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic group, respectively.…