Scattering in a Simple 2-d Lattice Model

TL;DR

This paper applies L"uscher's finite volume method to two 2D lattice models, including the Ising model, to extract scattering phase shifts and analyze lattice artifacts using Monte Carlo simulations.

Contribution

It demonstrates the application of L"uscher's method to 2D lattice models and investigates lattice effects on phase shifts with Monte Carlo techniques.

Findings

Successful extraction of phase shifts from finite volume spectra

Identification of O(a^2) lattice artifacts in the Ising model

Extension of the method to coupled Ising fields

Abstract

L\"uscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass and coupled through a 3-point term, both considered in the symmetric phase. The Monte Carlo simulation makes use of the cluster updating and reduced variance operator techniques. For the Ising system we study in particular O($a^2$) effects in the phase shift of the 2-particle scattering process.