  We propose a novel method to construct the Landau thermodynamic potential
directly from the fluctuations measured in heavy-ion collisions. The potential
is capable of revealing the signal of the critical end-point (CEP) and the
first order phase transition (FOPT) of QCD in the system even away from the
phase transition region. With the available experimental data, we show that the
criterion of the FOPT is negative for most of the collision energies which
indicates no signal of FOPT. The data at $\sqrt{s_\mathrm{NN}}=7.7$ GeV with
0-5% centrality shows a different behavior and the mean value of the data
satisfies the criterion. However, the uncertainty is still too large to make a
certain conclusion. The higher order fluctuations are also required for
confirming the signal. We emphasize therefore that new measurements with higher
precision for the $C_{1,...,6}$ within 0-5% centrality in the vicinity of
$\sqrt{s_\mathrm{NN}}=7.7$ GeV are in demand which may finally reveal the
signal of QCD phase transition.
