Exact solution (by algebraic methods) of the lattice Schwinger model in the strong-coupling regime

Details Exact solution (by algebraic methods) of the lattice Schwinger model in the strong-coupling regime Exact solution (by algebraic methods) of the lattice Schwinger model in the strong-coupling regime

1994-11-11

arxiv.org/abs/hep-lat/9411019v1

Phys.Rev. D51 (1995) 6417-6425

Physics

High Energy Physics

High Energy Physics - Lattice

22 pages (6 figures)

Scientific paper

10.1103/PhysRevD.51.6417

Using the monomer--dimer representation of the lattice Schwinger model, with $N_f =1$ Wilson fermions in the strong--coupling regime ($\beta=0$), we evaluate its partition function, $Z$, exactly on finite lattices. By studying the zeroes of $Z(k)$ in the complex plane $(Re(k),Im(k))$ for a large number of small lattices, we find the zeroes closest to the real axis for infinite stripes in temporal direction and spatial extent $S=2$ and 3. We find evidence for the existence of a critical value for the hopping parameter in the thermodynamic limit $S\rightarrow \infty$ on the real axis at about $k_c \simeq 0.39$. By looking at the behaviour of quantities, such as the chiral condensate, the chiral susceptibility and the third derivative of $Z$ with respect to $1/2k$, close to the critical point $k_c$, we find some indications for a continuous phase transition.

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