The Approach to the Thermodynamic Limit in Lattice QCD at μ\neq0

Abstract

The expectation value of the complex phase factor of the fermion determinant is computed to leading order in the $p$-expansion of the chiral Lagrangian. The computation is valid for $\mu <m_{\pi }/2$ and determines the dependence of the sign problem on the volume and on the geometric shape of the volume. In the thermodynamic limit with $L_i\to \infty$ at fixed temperature $1/L_0$, the average phase factor vanishes. In the low temperature limit where $L_i/L_0$ is fixed as $L_i$ becomes large the average phase factor approaches one. The results for a finite volume compare well with lattice results obtained by Allton {\it et al}.. After taking appropriate limits, we reproduce previously derived results for the $\epsilon$-regime and for 1-dimensional QCD. The distribution of the phase itself is also computed.

9 pages, 5 figures

References in corpus (5)

• The strongly interacting Quark Gluon Plasma, and the critical behaviour of QCD at imaginary chemical potential
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• The QCD Sign Problem for Small Chemical Potential
• Imaginary chemical potentials and the phase of the fermionic determinant
• The Sign Problem via Imaginary Chemical Potential

Cited by in corpus (9)

• Canonical partition function and finite density phase transition in lattice QCD
• Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
• A Random Matrix Study of the QCD Sign Problem
• Lattice QCD at finite temperature and density in the phase-quenched approximation
• Average phase factor in the PNJL model
• Distribution of Canonical Determinants in QCD
• Towards extremely dense matter on the lattice
• Triage of the Sign Problem
• How the Quark Number fluctuates in QCD at small chemical potential