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

TL;DR

This paper provides an exact algebraic solution for the lattice Schwinger model in the strong-coupling regime, analyzing phase transitions and critical behavior through partition function zeroes.

Contribution

It introduces an exact algebraic method to evaluate the partition function of the lattice Schwinger model at strong coupling, revealing critical points and phase transition characteristics.

Findings

Identification of the critical hopping parameter at about 0.39

Evidence for a continuous phase transition near the critical point

Analysis of partition function zeroes indicating phase transition behavior

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 $S\rightarrow \infty$ 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.