arXiv subjects

James C. Osborn

Publications and source records attributed to James C. Osborn.

42 records · Page 3Linked to original sources

arXiv2004

Universal results from an alternate random matrix model for QCD with a baryon chemical potential

We introduce a new non-Hermitian random matrix model for QCD with a baryon chemical potential. This model is a direct chiral extension of a previously studied model that interpolates between the Wigner-Dyson and Ginibre ensembles. We present exact results for all eigenvalue correlations for any number of quark flavors using the orthogonal polynomial method. We also find that the parameters of the model can be scaled to remove the effects of the chemical potential from all thermodynamic quantities until the finite density phase transition is reached. This makes the model and its extensions well suited for studying the phase diagram of QCD.

hep-th↗

arXiv2003

The QCD vacuum as a disordered medium: A simplified model for the QCD Dirac operator

We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the (dimensionless) Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling of the (dimensionless) Thouless energy in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.

hep-th↗

arXiv2003

Taste breaking in staggered fermions from random matrix theory

We discuss the construction of a chiral random matrix model for staggered fermions. This model includes $O(a^2)$ corrections to the continuum limit of staggered fermions and is related to the zero momentum limit of the Lee-Sharpe Lagrangian for staggered fermions. The naive construction based on a specific expansion in lattice spacing ($a$) of the Dirac matrix produces the term which gives the dominant contribution to the observed taste splitting in the pion masses. A more careful analysis can include extra terms which are also consistent with the symmetries of staggered fermions. Lastly I will mention possible uses of the model including studies of topology and fractional powers of the fermion determinant.

hep-lat↗

arXiv2001

Kosterlitz-Thouless Universality in a Fermionic System

A new extension of the attractive Hubbard model is constructed to study the critical behavior near a finite temperature superconducting phase transition in two dimensions using the recently developed meron-cluster algorithm. Unlike previous calculations in the attractive Hubbard model which were limited to small lattices, the new algorithm is used to study the critical behavior on lattices as large as $128\times 128$. These precise results for the first time show that a fermionic system can undergo a finite temperature phase transition whose critical behavior is well described by the predictions of Kosterlitz and Thouless almost three decades ago. In particular it is confirmed that the spatial winding number susceptibility obeys the well known predictions of finite size scaling for $T<T_c$ and up to logarithmic corrections the pair susceptibility scales as $L^{2-η}$ at large volumes with $0\leqη\leq 0.25$ for $0\leq T\leq T_c$.

cond-mat.str-el↗

arXiv2000

Critical Behavior of a Chiral Condensate with a Meron Cluster Algorithm

A new meron cluster algorithm is constructed to study the finite temperature critical behavior of the chiral condensate in a $(3+1)$ dimensional model of interacting staggered fermions. Using finite size scaling analysis the infinite volume condensate is shown to be consistent with the behavior of the form $(T_c-T)^{0.314(7)}$ for temperatures less than the critical temperature and $m^{1/4.87(10)}$ at the critical temperature confirming that the critical behavior belongs to the 3-d Ising universality class within one to two sigma deviation. The new method, along with improvements in the implementation of the algorithm, allows the determination of the critical temperature $T_c$ more accurately than was possible in a previous study.

hep-lat↗

arXiv1994

Surface Tension and Kinetic Coefficient for the Normal/Superconducting Interface: Numerical Results vs. Asymptotic Analysis

The dynamics of the normal/superconducting interface in type-I superconductors has recently been derived from the time-dependent Ginzburg-Landau theory of superconductivity. In a suitable limit these equations are mapped onto a ``free-boundary'' problem, in which the interfacial dynamics are determined by the diffusion of magnetic flux in the normal phase. The magnetic field at the interface satisfies a modified Gibbs-Thomson boundary condition which involves both the surface tension of the interface and a kinetic coefficient for motion of the interface. In this paper we calculate the surface tension and kinetic coefficient numerically by solving the one dimensional equilibrium Ginzburg-Landau equations for a wide range of $κ$ values. We compare our numerical results to asymptotic expansions valid for $κ\ll 1$, $κ\approx 1/\sqrt{2}$, and $κ\gg 1$, in order to determine the accuracy of these expansions.

cond-mat↗