Resolve symmetry breaking in the SMG phase

Determine whether any lattice symmetry breaks spontaneously in the symmetric-mass-generation phase of the four-flavour reduced-staggered model with source strength $h=2$, particularly at $(y,h)=(3.0,2)$, in the infinite-volume limit.

Background

The theorem establishes that every light mass-type bilinear has vanishing expectation value in a symmetry-preserving state, while spontaneous symmetry breaking could evade the corresponding conclusion. At $(3.0,2)$, the available $(4^4,8^4)$ comparison shows no inequivalent light mass channel growing faster than the free theory, and restricted like-for-like mode comparisons show decreasing susceptibility with volume.

The authors emphasize that the finite-volume evidence is insufficient to settle the issue. They identify a $12^4$ measurement as the concrete next test of the volume dependence.