Exact mass asymptotics for the two-dimensional O(4) lattice model

For the nearest-neighbor $O(4)$ model on the square lattice at inverse temperature β, we prove the exact low-temperature asymptotic $m_{\mathrm{lat}}(\beta )\sim 32\exp (\pi /4-1/2)\sqrt{\beta }\exp (-\pi \beta )(\beta \to \infty ).$ Here the mass is the gap of the full Osterwalder–Schrader transfer operator, including rotation-invariant local-observable sectors, in units of one original lattice time step.