The Phase Structure of the Weakly Coupled Lattice Schwinger Model
Abstract
The weak coupling expansion is applied to the single flavour Schwinger model with Wilson fermions on a symmetric toroidal lattice of finite extent. We develop a new analytic method which permits the expression of the partition function as a product of pure gauge expectation values whose zeroes are the LeeYang zeroes of the model. Application of standard finitesize scaling techniques to these zeroes recovers previous numerical results for the small and moderate lattice sizes to which those studies were restricted. Our techniques, employable for arbitrarily large lattices, reveal the absence of accumulation of these zeroes on the real hopping parameter axis at constant weak gauge coupling. The consequence of this previously unobserved behaviour is the absence of a zero fermion mass phase transition in the Schwinger model with single flavour Wilson fermions at constant weak gauge coupling.
 Publication:

arXiv eprints
 Pub Date:
 December 1998
 DOI:
 10.48550/arXiv.heplat/9812004
 arXiv:
 arXiv:heplat/9812004
 Bibcode:
 1998hep.lat..12004K
 Keywords:

 High Energy Physics  Lattice;
 Statistical Mechanics
 EPrint:
 8 pages, 2 figures, insert to figure 2 included