Topological charge in 1+1 dimensional lattice $φ^4$ theory

Details Topological charge in 1+1 dimensional lattice $φ^4$ theory Topological charge in 1+1 dimensional lattice $φ^4$ theory

2005-06-03

arxiv.org/abs/hep-lat/0506003v2

Phys.Rev. D72 (2005) 094504

Physics

High Energy Physics

High Energy Physics - Lattice

RevTex, 14 pages, 12 eps figures, minor changes

Scientific paper

10.1103/PhysRevD.72.094504

We investigate the topological charge in 1+1 dimensional $\phi^4$ theory on a lattice with Anti Periodic Boundary Condition (APBC) in the spatial direction. We propose a simple order parameter for the lattice theory with APBC and we demonstrate its effectiveness. Our study suggests that kink condensation is a possible mechanism for the order-disorder phase transition in the 1+1 dimensional $\phi^4$ theory. With renormalizations performed on the lattice with Periodic Boundary Condition (PBC), the topological charge in the renormalized theory is given as the ratio of the order parameters in the lattices with APBC and PBC. We present a comparison of topological charges in the bare and the renormalized theory and demonstrate invariance of the charge of the renormalized theory in the broken symmetry phase.

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