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

Abstract

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 $S\to \infty$ 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.

22 pages (6 figures)

References in corpus (1)

• Lee-Yang zeroes in the one flavour massive lattice Schwinger model

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