Control Experiments on Mass Generation in Discrete Field Models: Divergence, Local Coupling, and Spontaneous Symmetry Breaking
Year: 2026
Type: article
Abstract: In the preceding note [1], a discrete XY model on a three-dimensional cubic lattice wasconstructed. It yielded a static Coulomb limit, an orientational charge, and an emergentdefect mass m(β, Q) ≈ 0.126307 β Q2. However, the origin of the mass term μ2ϕ remainedopen. The present note presents three control numerical experiments that distinguish threequalitatively different situations: a divergence-type coupling of orientational variables tothe field, a local coupling of an auxiliary field to ϕ, and spontaneous symmetry breaking ina simplified scalar model. It is shown that the divergence-type coupling only renormalizesthe stiffness of the field; the local coupling produces a positive mass term at the cost ofexplicitly breaking the shift symmetry; and the vacuum expectation value mechanism inthe simplified model gives a mass proportional to ρ20. It is emphasized that the full Higgsmechanism with a local U (1) coupling is not tested in this note.
Author: Gromov, Alexey
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204197569