Family 215Probability and statistical mechanicsLeanNot yet digested
Canonical continuum limit and exact mass asymptotics
Constructs the canonical continuum limit of the two-dimensional nearest-neighbor model: a non-Gaussian local relativistic theory with a unique vacuum and a positive mass gap. For the square-lattice model, determines the exact leading asymptotic of the full transfer gap, . The family also proves exponential spin-correlation decay for two-dimensional nearest-neighbor models with n ≥ 3 at every positive temperature.
Manuscripts in this family · 5
The canonical massive continuum limit of the two-dimensional O(3) model
Oct 4, 2026·massive-continuum-o3.pdf
We construct a canonical interacting massive continuum limit of the two-dimensional nearest-neighbor model with unit-length spins, no external field, and no topological term. Normalized by susceptibility and second-moment correlation length, the limit exists as the bare coupling tends to infinity through all positive real values, without selecting subsequences. The limiting fields satisfy the Osterwalder–Schrader axioms and have a nonzero connected four-point correlation on separated time supports. Their reconstructed theory has a unique vacuum, a nonzero vacuum complement, and a positive Hamiltonian gap on that entire complement.
An Isolated Particle Pole for the Two-Dimensional O(3) Spin Field
Oct 4, 2026·o3-particle-pole.pdf
We consider the continuum spin field constructed from the nearest-neighbor two-dimensional model by the fixed prescription of the companion paper. We prove that its vector two-point spectral measure has a positive atom corresponding to the lowest mass, separated by a positive gap from all remaining mass support.
Exact mass asymptotics for the two-dimensional O(4) lattice model
Oct 5, 2026·exact-mass-o4.pdf
For the nearest-neighbor model on the square lattice at inverse temperature β, we prove the exact low-temperature asymptotic
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.
Sharp mass bounds for the two-dimensional O(4) model
Sep 23, 2026·paper.pdf
We prove sharp mass bounds for the two-dimensional nearest-neighbor model. For all sufficiently large inverse couplings β, the full transfer gap, including rotation-invariant local-observable sectors, is bounded above and below by positive multiples of . We also prove that the model has a unique periodic local limit and a positive full gap at every finite β > 0, resolving the all-temperature lattice mass-generation conjecture for this periodic state. Under the stated cutoff scaling, the mass bounds are uniform in independently fixed physical units. A continuum spectral interpretation requires separate convergence hypotheses for the transfer semigroup and the block observables.
Exponential decay in two-dimensional classical O(n) models
Sep 23, 2026·paper.pdfLean
We prove exponential decay of two-point correlations for the classical nearest-neighbor model on the square lattice, for every n ≥ 3 and every finite positive inverse temperature. The estimate is uniform over finite free-boundary subgraphs and bounded nonnegative edge strengths. This resolves positively the all-temperature exponential spin-decay conjecture for these models.