Related papers: Random Matrix Theory at Nonzero $\mu$ and $T$
Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model…
We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local…
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix…
Two aspects of the QCD phase diagrams are studied in the limit of a large number of colors: at zero temperature and nonzero density the (non)existence of nuclear matter, and at zero density and nonzero temperature the chiral phase…
In this talk we present the results published recently in Ref. [1], where we showed how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero…
We show that at the critical point of chiral random matrix models, novel scaling laws for the inverse moments of the eigenvalues are expected. We evaluate explicitly the pertinent microscopic spectral density, and found it in agreement with…
In this lecture we discuss correlations of the QCD Dirac eigenvalues. We find that below a scale of $E_c\sim \Lambda/L^2$ they are given by chiral Random Matrix Theory. This follows from analytical arguments based on partially quenched…
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…
Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain non-commutativity in the zero chemical potential limit and the thermodynamic limit when one tries to…
The chiral phase transition in the conventional random matrix model is the second order in the chiral limit, irrespective of the number of flavors N_f, because it lacks the U_A(1)-breaking determinant interaction term. Furthermore, it…
We describe our recent proposal that distinct phases of gauge theories with fundamental quarks translate into specific types of low-energy behavior in Dirac spectral density. The resulting scenario is built around new evidence…
We revisit the concept of chiral disorder in QCD in the presence of a QED magnetic field |eH|. Weak magnetism corresponds to |eH| < 1/rho^2 with rho\approx (1/3) fm the vacuum instanton size, while strong magnetism the reverse. Asymptotics…
Two-color finite density QCD is free from the sign problem, and it is thus regarded as a good model to check the validity of the analytic continuation method. We study the method in terms of the corresponding chiral random matrix model. It…
We reveal that the criticality of the chiral phase transition in QCD at the macroscale arises from the microscopic energy levels of its fundamental constituents, the quarks. We establish a novel relation between cumulants of the chiral…
For QCD at non-zero chemical potential $\mu$, the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from…
We propose a new method for simulating QCD at finite density, where interesting phases such as the color superconductivity phase is conjectured to appear. The method is based on a general factorization property of distribution functions of…
We study a random matrix model for QCD at finite density via complex Langevin dynamics. This model has a phase transition to a phase with nonzero baryon density. We study the convergence of the algorithm as a function of the quark mass and…
We investigate the QCD chiral phase transition at finite chemical potential $\mu$, using the renormalization group (RG) to characterize the infrared behavior of sigma models constrained by the flavor and spacetime symmetries. The results…
We discuss a random matrix theory that was originally constructed to describe two-color QCD at low density in the phase with a nonzero chiral condensate. With a particular choice of a parameter, the same random matrix theory also describes…
We investigate the QCD magnetic susceptibility chi at the finite quark-chemical potential (mu>0) and at zero temperature (T=0) to explore the pattern of the magnetic phase transition of the QCD vacuum. For this purpose, we employ the…