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- Which symmetry is being broken during a small/large AdS black hole phase transition using the Landau's phase transition approach?

I am trying to reproduce the results from this paper where they find out the expression for the Landau functional to be

$$\psi(x,t,p)=\frac{1}{4}(\frac{1}{x}+6x+px^3-4tx^2)$$

We plot the Landau functional v/s the order parameter($x$) at $p=0.5$ and obtain the Figure 4. from the paper as

Now according to free energy approach, this is a first-order phase transition. According to Landau theory, every phase transition is related to a symmetry breaking. Which symmetry is being broken here, for this system of AdS black holes?

$$\psi(x,t,p)=\frac{1}{4}(\frac{1}{x}+6x+px^3-4tx^2)$$

We plot the Landau functional v/s the order parameter($x$) at $p=0.5$ and obtain the Figure 4. from the paper as

Now according to free energy approach, this is a first-order phase transition. According to Landau theory, every phase transition is related to a symmetry breaking. Which symmetry is being broken here, for this system of AdS black holes?