Analysis of the Lee-Yang Zeros in Lattice Compact QED With Scalars and Fermions in 3D and in Lattice Non-Compact QED in 4D

Psycharis, Nektarios (1998) Analysis of the Lee-Yang Zeros in Lattice Compact QED With Scalars and Fermions in 3D and in Lattice Non-Compact QED in 4D. PhD thesis, University of Glasgow.

Abstract

Attempts to construct a theory with dynamical breaking of global chiral symmetries in four dimensions, which could explain or replace the Higgs-Yukawa mechanism of particle mass generation, usually lead to the introduction of a new strong gauge interaction beyond the standard model and its standard extensions. A lattice model with fermions and scalar fields and the compact U(l) gauge group, has been suggested in [1] as a promising candidate for such a prototype field theory on the lattice, and it is called the "chiU&phis; model" or QED with scalars and fermions. The chiral symmetry of this model is broken by the gauge interaction and restored by the light scalar. We investigate the critical behaviour of the three-dimensional lattice chiU&phis;3 model in the chiral limit. The model consists of a staggered fermion field, a U(1) gauge field (with coupling parameter (5) and a complex scalar field (with hopping parameter kappa). Two different methods are used: 1) fits of the chiral condensate and the mass of the neutral unconfined composite fermion to an equation of state and 2) finite size scaling investigations of the Lee-Yang zeros of the partition function in the complex fermion mass plane. For strong gauge coupling (beta ≤ 0.80) the critical exponents for the chiral phase transition are determined. We find strong indications that the chiral phase transition is in one universality class in this beta interval: that of the three-dimensional Gross-Neveu model with two fermions. Thus the continuum limit of the chiU&phis;3 model defines here a nonperturbatively renormalizable gauge theory with dynamical mass generation. At weak gauge coupling and small ac, we explore a region in which the mass in the neutral fermion channel is large but the chiral condensate on finite lattices very small. If it does not vanish in the infinite volume limit, then a continuum limit with massive unconfined fermion might be possible in this region, too. Calculations of the Lee-Yang zeros of the partition function in the complex fermion mass plane, were performed in [40] in order to help to clarify the position of the critical point and the critical exponent of the transition of non-compact QED. However, exploratory simulations[39] of this theory on a 64 lattice showed that these zeros appeared to depend on the "updating" mass at which the ensemble they are found from is generated. This dependence is incorrect Although we used a multi-precision package for the calculation of the Lee-Yang zeros, our analysis confirmed the dependence of the Lee-Yang zeros on the "updating" mass on a lattice. High statistics simulations on large lattices, are probably necessary in order to verify the absence of the dependence of the edge singularity on the update mass at which the ensemble it is found from is generated.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: Ian Barbour
• Keywords: Theoretical physics
• Date of Award: 1998
• Depositing User: Enlighten Team
• Unique ID: glathesis:1998-75429
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 19 Nov 2019 20:08
• Last Modified: 19 Nov 2019 20:08
• URI: https://theses.gla.ac.uk/id/eprint/75429