CM In the literature: contested

Is the pseudogap temperature T* a thermodynamic phase transition

In plain words

If the pseudogap is a true phase, crossing its boundary should leave a mark in heat capacity, as freezing does for water; no such mark has been clearly seen.

Precise statement

In a clean hole-doped cuprate (YBa2Cu3O6+x or HgBa2CuO4+d), determine whether the free energy is nonanalytic along T*(p): resolve a specific-heat or thermal-expansion anomaly at T* matching the symmetry breaking claimed by polarized neutron scattering, torque magnetometry and polar Kerr rotation, or bound $\Delta C/T$ below the value required by a mean-field transition with the claimed order parameter. An answer is a detected singularity with its exponent, or such a bound.

What would settle it

High-resolution calorimetry or thermal expansion through $T*$ on crystals in which torque or neutron onsets are measured on the same piece.

Status in the literature

Resonant ultrasound (2013) found an elastic anomaly along T*(p), and torque magnetometry (2017) and polarized neutron data indicate symmetry breaking near T*, but no calorimetric anomaly at T* has been resolved and the neutron results are disputed.