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 Nf = 1 Wilson fermions in the strong-coupling regime (P = 0), we evaluate its partition function Z exactly on finite lattices. By studying the zeros of Z(k) in the complex plane (Re(k),Im(k)) for a large number of small lattices, we find the zeros closest to the real axis for infinite strips in the 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 + oo on the real axis a t about kc E 0.39. By looking at the behavior 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 kc, we find some indications for a continuous phase transition.

Critical behavior of the Schwinger model with Wilson fermions

“…Figures 4a,b contain the results for the susceptibility (8) at two typical values of the gauge coupling β against κ in 8 2 , 12 2 , 16 2 , 20 2 and 24 2 lattices. As expected for a real phase transition, the susceptibility shows a well defined maximum at some critical value κ c , the height of these peaks increasing with the lattice size and eventually diverging in the infinite volume limit.…”

Strong coupling lattice Schwinger model on large spherelike lattices

“…For better comparison with earlier work 8,9] we analyze the position of the zero in the variable . Table 1 and g. 5 give { for the lattices studied { those zeros in the complex variable closest to the real axis.…”

Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

“…In recent years dual representations have been successfully used to overcome complex action problems for a variety of lattice field theories (see, e.g., the reviews [1][2][3][4][5]). For further developing these techniques the Schwinger model is a particularly interesting system (see [6][7][8][9][10][11][12][13][14][15] for related examples) since in the conventional representation it suffers from a complex action problem coming from two sources: a topological term, as well as finite density (in the two flavor model). Furthermore, the relativistic fermions lead to additional minus signs in the dualization.…”