Complex Zeros of the Partition Function in Lattice Quantum Chromodynamics

[摘要] The theory of Lee and Yang, which relates the distribution of the zeros of the partition function to the phase structure of a system, is applied to lattice field theory with dynamical fermions. A method is described in which the partition function is evaluated as a finite polynomial in either the bare fermion mass or the 'fugacity'. The roots of this polynomial which are relevant to the physics, i. e. those close to the real axis, are then studied. The partition function zeros are first studied in the fermion mass plane for SU(3), SU(2) and U(1) gauge theories with four flavours of staggered fermions in the infinite coupling limit. Differences are observed in the distributions of zeros on finite lattices, but all are consistent with the expected critical point at ma = 0 on an infinite lattice. The SU(3) and U(1) calculations are then extended to weaker couplings and, in the SU(3) case, to larger systems. In Chapter 7 we perform the expansion in the fugacity plane. The Grand Canonical Partition Function is expanded in terms of Canonical Partition Functions for fixed fermion number. The distributions of zeros give strong evidence for the existence,or otherwise, of a phase transition at finite chemical potential.

[发布机构] University:University of Glasgow

[关键词] Theoretical physics