Landau theory: why does a m^3 term implies first order transition phase

[IRobot]

Hi,

I am not sure it is the right subcategory to post a question on statistical physics. But anyway, I read a couple of times that adding a m^3 to the Landau free energy implies that we may observe a first order transition phase, but I don't see why. Maybe it does imply some discontinuity in the entropy, latent heat, but I am not seeing that.

 

[DrDu]

Hi,

I am not sure it is the right subcategory to post a question on statistical physics. But anyway, I read a couple of times that adding a m^3 to the Landau free energy implies that we may observe a first order transition phase, but I don't see why. Maybe it does imply some discontinuity in the entropy, latent heat, but I am not seeing that.

What is m? Mass, magnetic moment?

 

[IRobot]

M is the magnetic moment, the order parameter.

 

[mathfeel]

Hi,

I am not sure it is the right subcategory to post a question on statistical physics. But anyway, I read a couple of times that adding a m^3 to the Landau free energy implies that we may observe a first order transition phase, but I don't see why. Maybe it does imply some discontinuity in the entropy, latent heat, but I am not seeing that.

Try to make a plot of a sample free energy:
$F=t m^2 + b m^3 + m^4$
for different values of t and b? In particular, try a fixed t at some finite value and varies b.

When t >> b, the free energy is minimum is at m=0, then as you increase b, at some point, the minimum JUMPS from 0 to some finite value. That, by definition, is a first order transition where the order parameter has a discontinuous jump.

 

[IRobot]

Thanks, you made it clear ;)