Distribution Of Yang-Lee Zeros Research Articles

Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods

The distribution of Yang-Lee zeros in the ferromagnetic Ising model in both two and three dimensions is studied on the complex field plane directly in the thermodynamic limit via the tensor network methods. The partition function is represented as a contraction of a tensor network and is efficiently evaluated with an iterative tensor renormalization scheme. The free-energy density and the magnetization are computed on the complex field plane. Via the discontinuity of the magnetization, the density of the Yang-Lee zeros is obtained to lie on the unit circle, consistent with the Lee-Yang circle theorem. Distinct features are observed at different temperatures---below, above and at the critical temperature. Application of the tensor-network approach is also made to the $q$-state Potts models in both two and three dimensions and a previous debate on whether, in the thermodynamic limit, the Yang-Lee zeros lie on a unit circle for $q>2$ is resolved: they clearly do not lie on a unit circle except at the zero temperature. For the Potts models (q=3,4,5,6) investigated in two dimensions, as the temperature is lowered the radius of the zeros at a fixed angle from the real axis shrinks exponentially towards unity with the inverse temperature.

Random matrix theory and QCD at nonzero chemical potential

In this lecture we give a brief review of chiral Random Matrix Theory (chRMT) and its applications to QCD at nonzero chemical potential. We present both analytical arguments involving chiral perturbation theory and numerical evidence from lattice QCD simulations showing that correlations of the smallest Dirac eigenvalues are described by chRMT. We discuss the range of validity of chRMT and emphasize the importance of universality. For chRMT's at μ ≠ 0 we identify universal properties of the Dirac eigenvalues and study the effect of quenching on the distribution of Yang-Lee zeros.

Fermion determinants in matrix models of QCD at nonzero chemical potential

The presence of a chemical potential completely changes the analytical structure of the QCD partition function. In particular, the eigenvalues of the Dirac operator are distributed over a finite area in the complex plane, whereas the zeros of the partition function in the complex mass plane remain on a curve. In this paper we study the effects of the fermion determinant at a nonzero chemical potential on the Dirac spectrum by means of the resolvent $G(z)$ of the QCD Dirac operator. The resolvent is studied both in a one-dimensional U(1) model (Gibbs model) and in a random matrix model with the global symmetries of the QCD partition function. In both cases we find that, if the argument $z$ of the resolvent is not equal to the mass $m$ in the fermion determinant, the resolvent diverges in the thermodynamic limit. However, for $z=m$ the resolvent in both models is well defined. In particular, the nature of the limit $z\ensuremath{\rightarrow}m$ is illuminated in the Gibbs model. The phase structure of the random matrix model in the complex $m$ and \ensuremath{\mu} planes is investigated both by a saddle point approximation and via the distribution of Yang-Lee zeros. Both methods are in complete agreement and lead to a well-defined chiral condensate and quark number density.

On the Yang-Lee Distribution of Zeros for a Gas Obeying van der Waals' Equation of State. III: Calculations for Low Temperatures

On the Yang-Lee Distribution of Zeros for a Gas Obeying van der Waals' Equation of State. III: Calculations for Low Temperatures

On the Yang-Lee Distribution of Zeros for a Gas Obeying van der Waals' Equation of State. II: General Considerations for All Temperatures

On the Yang-Lee Distribution of Zeros for a Gas Obeying van der Waals' Equation of State. II: General Considerations for All Temperatures

On the Yang-Lee Distribution of Zeros for a Gas Obeying van der Waals' Equation of State. I: Fundamental Concepts and the Limit of Vanishing Attraction

On the Yang-Lee Distribution of Zeros for a Gas Obeying van der Waals' Equation of State. I: Fundamental Concepts and the Limit of Vanishing Attraction

The Yang-Lee distribution of zeros for a classical one-dimensional fluid

The Yang-Lee distribution of zeros for a classical one-dimensional fluid

The Yang-Lee distribution of zeros for a classical one-dimensional fluid

The interaction potential is assumed to satisfy (γ) = + infinity if γ 2a, where a is a constant greater than zero, so that only nearest neighbours can interact. At any fixed temperature T let kTπ(z) be the thermodynamic pressure at fugacity z gt-or-equal, slanted 0, as calculated from the equation of state. Let Π (z) be the complete analytic function obtained by analytic continuation of π(z) into the complex z plane, and G be the set of values of z for which one branch of Π (z), say Π max(z), is regular and has a larger real part than all the others. It is proved that, in the limit where the length L of the system tends to infinity, the zeros of the grand partition function Ξ (z, L) approach a point set Z which consists of analytic arcs and is the complement of G. It is also proved that G is simply connected, that for all z in G, and that the limiting line density of zeros of Ξ along any arc of Z (each zero being given the weight L−1) is (2π)−1 times the discontinuity in Imπmax(z) across the arc. As an illustration, (a result of Hemmer et al.), that Z is - infinity < z less-than-or-eq, slant -1/ea for the hard-rod system is confirmed rigorously.

Calculation of the Yang-Lee Distribution of Zeros

Calculation of the Yang-Lee Distribution of Zeros