Scaling hypothesis and nonzero-field critical invariants

Assuming the static scaling hypothesis, a proof is given for the existence of invariants (Q) associated with the extrema of the thermodynamic functions: nonzero-field susceptibility, nonzero-field specific heat, nonzero-wave-vector correlation function. In the framework of the Landau theory, the value of the invariant Q related to the susceptibility is found to be Q=2. Experimental measurements of the maxima of the nonzero-electric-field susceptibility for a ferroelectric triglycine sulfate TGS crystal give a value 1.87±{}0.05 for the invariant Q. This result provides new evidence of a deviation from Landau theory in the thermodynamic behavior of the TGS crystal.