Recent content by muzialis

Hi All, I am desperate to understand a calculation presented in a paper by Sethna, "Elastic theory has zero radius of convergence", freely available online $$ lim_{\epsilon \to +0}Z(-P+i\epsilon) = lim_{\epsilon \to +0} \int_{0}^{\infty} \mathrm{d}x \, \int_{0}^{\infty} \mathrm{d}y \exp \{...

Thanks a lot. This discussion was very useful to me.

Thanks for your reply. Maybe (probably) I am a little slow, but I dare say I do not see how your comment answers my question. I know that A(T, V, N) = −k(B). T. lnZ and in all textbooks it is shown how this expression coincides with the "classical" one, A = {E} - TS. My question is, by looking...

I am afraid I still have issues on the matter. Now I understand that average energy and temperature are related. So in my canonical System the temperature, and hence the average energy, are constant. By Definition, the free energy is constant. The latter equals A = {E} - TS, where {} is used to...

Thank you for your help. So number 2 is the one I misunderstood. 3) is probably bad language from my side. Maye something like, "the probability of the ideal gas to be in a certain microstate with a certain energy E, follows Boltzmann's distribution".

Thanks for your reply but regretfully I do not understand. The equation was wrong indeed, the correct one is $E = 3NkT/2$. Having said this, I do not follow your Argument. You say " In statistical mechanics, if the system have a well defined temperature, its total energy E must fluctuate", this...

Thanks for your reply. I am not so sure I understand it though. While I understand what a mean energy can be, I am not familiar at all with "mean temperature" in the canonical Setting. the temperature as I understand it should be fixed by the bath. Why is the Expression I quote for energy...

I must be missing some point with regards to the canonical Distribution. Let us imagine I have a closed (to energy and matter) box full of ideal gas at temperature T. The total energy in the box equals hence E=3N2kT , where N is the number of molecules, k Boltzmann's connstant.Next, I allow the...

I think the "geometrical interpretation" is the fact that the Ramahujan summation gives the first term in an asymptotic series related to the divergent sum. The matter is explained best here...

Hi All, reading a paper by Langer (Theory of the Condensation Point, Annals of Physics 41, 108-157, 1967), I came across an analytical continuation technique which I do not understand (would like to upload the paper PDF but I am not so sure this is allowed). Essentially, he deals with the...

Thanks for the advice, will do so.

I am not convinced at all that "a thermometer measures only the translational degrees of freedom". If one goes back to the basics, I think the matter is very clear. I have a box containing an ideal gas, at a volume, pressure, temperature. Now I contact it with a thermometer. They will reach...

Hi All, reading a paper by Langer (Theory of the Condensation Point, Annals of Physics 41, 108-157, 1967), I came across an analytical continuation technique which I do not understand (would like to upload the paper PDF but I am not so sure this is allowed). Essentially, he deals with the...

Hi all, I am struggling to grasp the sense of the partition function. First of all, I had a look at a couple of derivations (which the relevant Wikipedia page follows) in which the concept of heat"energy of a thermal bath" is invoked. Well this is already confusing me: if the thermal bath has an...

Very usefuland interesting, many thanks to all.