Different orders for a phase transition (variable depending)

[lfqm]

Hi guys!
I've got this system in which Eherenfest classification of "order" is assumed to be ok.
So I took my free energy function $$G(T,P)$$ and start differentiating.
I found just one phase transition between two phases, the problem is the phase transition is of different order depending on the variable, i.e. the lowest derivative respect to T to be discontinuous is the first, but the lowest derivative respect to P to be discontinuous is the second...

So... Is this normal?, I though it didn't matter how I cross the boundary between the phases, but apparently it does.
What is the order if the transition?, first (it is the lowest)?

Thanks

 

[AndyW]

for sharing your findings!

Hello,

Thank you for sharing your findings with us. It is interesting that you have observed a phase transition with different orders depending on the variable. This is not uncommon in complex systems, and it is known as a mixed-order phase transition.

In mixed-order phase transitions, the order of the transition depends on the path taken to cross the boundary between phases. This means that the transition can be first-order for one variable and second-order for another. This is due to the fact that the system is sensitive to changes in different variables in different ways.

In your case, it seems that the first-order transition occurs for the variable T, while the second-order transition occurs for the variable P. This is completely normal and does not affect the validity of the Eherenfest classification of order. The classification is based on the behavior of the thermodynamic variables near the critical point, and in your case, both transitions still exhibit the characteristic behavior of a first-order and second-order transition, respectively.

I hope this helps to clarify your findings. Keep up the good work in your research!