Pointwise thermodynamic extrapolation of the rescaled MT diagnostic

Determine the pointwise thermodynamic extrapolation of the rescaled Mandelstam–Tamm diagnostic over the Floquet Ising parameter plane.

Background

The paper studies the size-normalized Mandelstam–Tamm diagnostic for a disordered Floquet Ising chain using finite system sizes, finite observation windows, and finite parameter grids. Although the path-averaged energy dispersion is numerically consistent with leading square-root system-size scaling, the authors emphasize that the endpoint angle and finite-size correction terms remain size dependent.

Consequently, the available calculations do not resolve the pointwise thermodynamic behavior of the full rescaled MT diagnostic across parameter space. Establishing this behavior would require controlled finite-size extrapolation beyond the accessible sizes and correction-form uncertainties.

References

The phase-resolved analysis is restricted to the accessible finite sizes, leaving pointwise thermodynamic extrapolation unresolved.

— Rescaled Mandelstam Tamm characterization of discrete time crystal response in a disordered Floquet Ising chain  (2608.19403 - Naqash et al., 19 Aug 2026) in Section 4, Finite-size and phase-resolved structure of the rescaled MT diagnostic

The data therefore identify finite-size DTC-like, localized non-DTC, and thermal-like sectors but do not determine a thermodynamic three-phase diagram.

— Rescaled Mandelstam Tamm characterization of discrete time crystal response in a disordered Floquet Ising chain  (2608.19403 - Naqash et al., 19 Aug 2026) in Section 5.2, Comparison with response and spectral crossovers