Determine thermodynamic convergence of interacting channel concentrations

Determine whether the finite-size channel-concentration sequences for the critical three-state Potts chain and the nonintegrable next-nearest-neighbor transverse-field Ising model converge in the thermodynamic limit under their respective many-body level-projector resolutions and response-probe specifications.

Background

The paper compares finite-size interacting response distributions with two types of references. The critical three-state Potts thermal response is compared with a descendant-resolved conformal-field-theory concentration and an exponent-only odd-ladder approximation, while the next-nearest-neighbor transverse-field Ising response is compared with the exact finite-size transverse-field Ising sequence. These calculations use many-body energy-level projectors rather than the momentum-block resolution used in the exactly solvable free chains.

Although the finite-size data show trends toward the stated references, the accessible system sizes, unresolved spectral tails, projector-resolution issues, and possible correction hierarchies prevent the authors from establishing convergence as system size tends to infinity. The problem is therefore to determine the actual thermodynamic limits of both interacting sequences under the declared observables.