Related papers: Critical Scaling at Zero Virtuality in QCD
We formulate a random matrix model which mimics the chiral phase transition in QCD with two light flavors. Two critical exponents are calculated. We obtain the mean field values $\beta = \frac 12 $ and $\delta = 3$. We also find that the…
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the…
Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this review, we discuss both types of applications of…
We present numerical evidences for the logarithmic scaling of the entanglement entropy in critical random spin chains. Very large scale exact diagonalizations performed at the critical XX point up to L=2000 spins 1/2 lead to a perfect…
The Helmholtz free energy density is parametrized as a function of temperature and baryon density near the chiral critical point of QCD. The parametrization incorporates the expected critical exponents and amplitudes. An expansion away from…
We use the linear sigma model with quarks to study the QCD phase diagram from the point of view of chiral symmetry restoration. We compute the leading order effective potential for high and low temperatures and finite quark chemical…
We investigate the evolution of entanglement spectra under a global quantum quench from a short-range correlated state to the quantum critical point. Motivated by the conformal mapping, we find that the dynamical entanglement spectra…
The investigation of remnants associated with the QCD chiral critical point is a primary objective in high-energy ion collision experiments. Numerous studies indicate that a scaling relation between higher-order factorial moments of hadron…
We calculate the renormalization group flows of all perturbatively renormalizable interactions in the three-dimensional Ginzburg-Landau potential for the chiral phase transition of three-flavor quantum chromodynamics. On the contrary to the…
We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynamic limit we find that the distribution of the eigenvalues in…
Critical exponents have been obtained for a 3D spin particle system. Clusters are formed and system reaches a critical behavior when fragment size distribution follows a power law, as predicted by Fisher Liquid Droplet Model. Also,…
The inverse eigenvalues of the Dirac operator in the Schwinger model satisfy the same Leutwyler-Smilga sum rules as in the case of QCD with one flavor. In this paper we give a microscopic derivation of these sum rules in the sector of…
In these lectures we review recent results on universal fluctuations of QCD Dirac spectra and applications of Random Matrix Theory (RMT) to QCD. We review general properties of Dirac spectra and discuss the relation between chiral symmetry…
We propose that nonequilibrium quantum criticality in open systems at both zero and finite temperatures can be described by a master equation of the Lindblad form. We derive this equation from a system coupling microscopic to a heat bath.…
We study the effect of topology for a random matrix model of QCD at nonzero imaginary chemical potential or nonzero temperature. Non-universal fluctuations of Dirac eigenvalues lead to normalization factors that contribute to the…
A general class of inverse-moment sum rules was previously derived by the authors in a chiral perturbation theory (ChPT) study at two-loop order of the isospin and hypercharge vector-current propagators. Here, we address the evaluation of…
We study lattice QCD in the limit that the quark mass and chemical potential are simultaneously made large, resulting in a controllable density of quarks which do not move; this is similar in spirit to the quenched approximation for zero…
I review recent lattice results on strongly interacting matter under extreme conditions, with emphasis on the finite-temperature QCD transition at $\mu_B=0$, its approach toward the chiral limit and the fate of the $U_A(1)$ anomaly, as well…
We study QCD at finite temperature and non-zero chemical potential to derive the critical temperature at the chiral phase transition (crossover). We solve a set of Dyson--Schwinger partial differential equations using the exact solution for…
Spin-glass (SG) and chiral-glass (CG) orderings in three dimensional (3D) Heisenberg spin glass with and without magnetic anisotropy are studied by using large-scale off-equilibrium Monte Carlo simulations. A characteristic time of…