Thermodynamic Limit: Compute & Understand Model

[Euclid]

Can someone give an example of how to compute the "thermodynamic limit" of some model? I am very confused by this concept.

 

[mrandersdk]

I guess it is just making the number of particles in your system infinity, then depending on what you desripe you have to make som restrains on how you take this limit, one example could be to keep the density if the system constant that is, when N -> inf, the vomule go to infinity to in such a way that N/V is constant.

This can seems strange because we never going to have a infinity large system with infinity volume, but this is a good aproximation of a system that have particle numbers in the range of avogadros number and a volume there is a lot bigger than the particles in the system.

 

[Euclid]

I guess it is just making the number of particles in your system infinity, then depending on what you desripe you have to make som restrains on how you take this limit, one example could be to keep the density if the system constant that is, when N -> inf, the vomule go to infinity to in such a way that N/V is constant.

This can seems strange because we never going to have a infinity large system with infinity volume, but this is a good aproximation of a system that have particle numbers in the range of avogadros number and a volume there is a lot bigger than the particles in the system.

I guess I am confused mostly as to why it sometimes doesn't exist. In given situation, I would like to know how to determine if the TL exists. When exactly is it appropriate to take this limit?

Also, related to this, does anyone know what "surface effects" are?

 

[mrandersdk]

the thing is you often get some formel where you have N/V in it, then you could take the limit so this is constant, if it is N^2/V that are in your formel you take the limit such that this is constant, if you took the limit in that case such that N/V is constant then this would make the formel go to infinity and then meaningless.

you could also look at http://en.wikipedia.org/wiki/Thermodynamic_limithttp://en.wikipedia.org/wiki/Thermodynamic_limit which try to explain why we want to make the limit.

surface effects, i guess depend on the context, but if you fx. have a solid, then we often approximate this by an infinite solid, because that enables us to make our potential periodic, that is impose bondary conditions: V(x) = V(x-a), where 'a' i a lattice constant, in the x,y, and z direction (assuming that the solid lattice is square). This is in genneral a good approximation beacuse most atoms in the lattice are inside the solid so most see this potential, but the atoms near the surface see a different potential so there the model brakes down, because of the surface, thus a surface effect.