arXiv subjects

M. A. Stephanov

Publications and source records attributed to M. A. Stephanov.

45 records · Page 3Linked to original sources

arXiv1998

On the Phase Diagram of QCD

We analyze the phase diagram of QCD with two massless quark flavors in the space of temperature, T, and chemical potential of the baryon charge, mu, using available experimental knowledge of QCD, insights gained from various models, as well as general and model independent arguments including continuity, universality, and thermodynamic relations. A random matrix model is used to describe the chiral symmetry restoration phase transition at finite T and mu. In agreement with general arguments, this model predicts a tricritical point in the T mu plane. Certain critical properties at such a point are universal and can be relevant to heavy ion collision experiments.

hep-ph↗

arXiv1998

Critical region of the finite temperature chiral transition

We study a Yukawa theory with spontaneous chiral symmetry breaking and with a large number N of fermions near the finite temperature phase transition. Critical properties in such a system can be described by the mean field theory very close to the transition point. We show that the width of the region where non-trivial critical behavior sets in is suppressed by a certain power of 1/N. Our Monte Carlo simulations confirm these analytical results. We discuss implications for the chiral phase transition in QCD.

hep-lat↗

arXiv1998

The Phase Diagram of QCD

We show that current experimental knowledge of QCD together with general model independent arguments such as continuity, universality and thermodynamic relations, as well as the information gained from various models can be used to constrain the phase diagram of QCD as a function of temperature and baryon chemical potential.

hep-ph↗

arXiv1996

Dirac operator as a random matrix and the quenched limit of QCD with chemical potential

The behavior of quenched QCD at nonzero chemical potential $μ$ has been a long-standing puzzle. An explicit solution is found using the random matrix approach to chiral symmetry breaking. At nonzero $μ$ the quenched QCD is not a simple $n\to0$ limit of a theory with $n$ quarks: a naive `replica trick' fails. A limit that leads to the quenched QCD is that of a theory with $2n$ quarks: $n$ quarks with original action and $n$ quarks with conjugate action.

hep-lat↗

arXiv1996

Random matrix model of QCD at finite density and the nature of the quenched limit

We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential $μ$. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails for $μ\neq0$: we find that quenched QCD is not a simple $n\to0$ limit of QCD with $n$ quarks. It is the limit of a theory with $2n$ quarks: $n$ quarks with original action and $n$ quarks with conjugate action. The results agree with earlier studies of lattice QCD at $μ\neq0$ and provide a simple analytical explanation of a long-standing puzzle.

hep-lat↗

arXiv1996

Chiral symmetry at finite T, the phase of the Polyakov loop and the spectrum of the Dirac operator

A recent Monte Carlo study of {\em quenched} QCD showed that the chiral condensate is non-vanishing above $T_c$ in the phase where the average of the Polyakov loop $P$ is complex. We show how this is related to the dependence of the spectrum of the Dirac operator on the boundary conditions in Euclidean time. We use a random matrix model to calculate the density of small eigenvalues and the chiral condensate as a function of $\arg P$. The chiral symmetry is restored in the $\arg P=2π/3$ phase at a higher $T$ than in the $\arg P=0$ phase. In the phase $\arg P = π$ of the $SU(2)$ gauge theory the chiral condensate stays nonzero for all~$T$.

hep-lat↗

arXiv1995

Dimensional Reduction and Quantum-to-Classical Reduction at High Temperatures

We discuss the relation between dimensional reduction in quantum field theories at finite temperature and a familiar quantum mechanical phenomenon that quantum effects become negligible at high temperatures. Fermi and Bose fields are compared in this respect. We show that decoupling of fermions from the dimensionally reduced theory can be related to the non-existence of classical statistics for a Fermi field.

hep-ph↗

arXiv1994

On the equivalence between 2D Yukawa and Gross-Neveu models

We study numerically on the lattice the 2D Yukawa model with the U(1) chiral symmetry and $N_F$ = 16 at infinite scalar field self-coupling. The scaling behaviour of the fermion mass, as the Yukawa coupling approaches zero, is analysed using the mean field method. It is found to agree with that of the Gross-Neveu model with the same symmetry and $N_F$. The results suggest that the 2D Yukawa models belong to the universality class of the Gross-Neveu models not only at weak scalar field self-coupling but also for a broad range of the bare parameters which is not accessible to the $1/N_F$ expansion. New universality classes might arise at the crossover to the spin model universality class, however.

hep-lat↗

arXiv1993

Study of the Asymptotic Freedom of 2D Yukawa Models on the Lattice

We investigate on the lattice the Yukawa models in 2 dimensions with Z(2) and U(1) symmetries. These models reduce to the usual and chiral Gross-Neveu models, respectively, when the kinetic and the selfcoupling terms of the scalar field are turned off. The numerical data and mean field arguments suggest that, at least for some range of the scalar field hopping parameter, fermion mass is dynamically generated for arbitrarily weak Yukawa coupling. The models are asymptotically free in this coupling, like the Gross-Neveu models, even when the scalar quartic selfcoupling is strong.

hep-lat↗