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

Nov, 1994
21 pages
Published in:
  • Phys.Rev.D 51 (1995) 6417-6425
e-Print:
DOI:
Report number:
  • BI-TP-94-54
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Abstract: (DESY)
Using the monomer--dimer representation of the lattice Schwinger model, with Nf=1N_f =1 Wilson fermions in the strong--coupling regime (β=0\beta=0), we evaluate its partition function, ZZ, exactly on finite lattices. By studying the zeroes of Z(k)Z(k) in the complex plane (Re(k),Im(k))(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=2S=2 and 3. We find evidence for the existence of a critical value for the hopping parameter in the thermodynamic limit S→∞S\rightarrow \infty on the real axis at about kc≃0.39k_c \simeq 0.39. By looking at the behaviour of quantities, such as the chiral condensate, the chiral susceptibility and the third derivative of ZZ with respect to 1/2k1/2k, close to the critical point kck_c, we find some indications for a continuous phase transition.
  • Schwinger model
  • dimension: 2
  • lattice field theory
  • partition function
  • approximation: strong coupling
  • strong coupling: approximation
  • algebra: mathematical methods
  • numerical calculations: Monte Carlo