Strong coupling lattice Schwinger model on large spherelike lattices

Abstract

The lattice regularized Schwinger model for one fermion avor and in the strong coupling limit is studied through its equivalent representation as a restricted 8-vertex model. The Monte Carlo simulation on lattices with torus-topology is handicapped by a severe non-ergodicity of the updating algorithm; introducing lattices with spherelike topology avoids this problem. We present a large scale study leading to the identi cation of a critical point with critical exponent = 1, in the universality class of the Ising model or, equivalently, the lattice model of free fermions.

Grassmann tensor renormalization group approach to one-flavor lattice Schwinger model

“…It should be noted that our result for κ c ð∞Þ is also consistent with κ c ¼ 0.3805ð1Þ in Ref. [2] and κ c ¼ 0.3806641ð78Þ translated from m c in Ref. [3].…”

“…The similar situation is also found with a different choice of the boundary condition in Ref. [2]. In conclusion, our results indicate a second-order phase transition with α ≃ 0 and ν ¼ 1 so that the one-flavor lattice Schwinger model belongs to the 2D Ising universality class even at finite coupling.…”

“…In the strong coupling limit at β ¼ 0.0, the oneflavor lattice Schwinger model was shown to be mapped to an eight-vertex model [1]. This was followed by large-scale Monte Carlo simulations on spherelike lattices [2] and with a method extending the worm algorithm [3], both of which have proved that this model also lies in the 2D Ising universality class. One may naively expect that a phase transition line runs from β ¼ 0.0 to ∞ belonging to the 2D Ising universality class.…”

Chiral symmetry in the 2-flavour lattice Schwinger model

“…leads to an SU (2) A lattice operator identity analogous to (7). In order to satisfy that relation non-trivially we choose to take expectation values with regard to a pion source and obtain ; the value for the 1-flavour model is from [7].…”

Spin and gauge systems on spherical lattices

“…In the thermodynamic limit at the critical point the manifold becomes flat and should lead to a universal field theory independent of the details of the boundary conditions. Other 2D studies on similar lattices include random as well as tetrahedral lattices [5,6] and a recent investigation of the 7-vertex model (the strong coupling Schwinger model) for a pillow-like topology [7].…”