would it be possible to rearrange your lectures? if you put them in playlist, it would be much easier to know which lecture one has to watch first thanks in advance
Very nice video introducing the subject. I struggled with it on scientific articles, but this has helped me a lot. I am very curious on model-specific solutions away from the critical point. I am curious if it can replicate the "sigmoidal"-esque behavior that many order parameters seem to show. I will watch the other videos on the subject!
Many thanks. This has been the clearest explanation of the renormalization techniques I have ever learned about. One question remains for me. Kadanoff (2000, p.238) says that "The existence of a phase transition requires an infinite system. No phase transitions occur in systems with a finite number of degrees of freedom." Can you please tell me how this fits into your discussion about the analysis of critical phase transition? (which minutes of your talk relate to this statement)? Huge thanks in advance, Olga.
Dear Olga, nice that you enjoy the video. For the answer to your question, I refer to my video on the Ising model, ruclips.net/video/hX_FrS5XO3I/видео.html, around minute 8.
Dear Somesh, thank you for your kind words. I think the best would be my video on the Ising model, see ruclips.net/video/hX_FrS5XO3I/видео.html Best regards, Jos
Thanks for your question. The interaction between the t^k depends on the Hamiltonian of the s_i. It is not always easy to find it, but for the Ising model as in this case, it is assumed that the 'renormalised' interaction (between the t^k) only acts between nearest neighbours and then you can work it out, e.g. numerically. That is not the point of this movie. To see how such a procedure is carried out for the Ising model on a triangular lattice, see e.g. my video on real space renormalisation.
Thanks for the detailed explanation. I have one confusion. In the derivation of the correlation function exponent, how do you get a factor r^(d-1) in the radial integral. Please explain
The integral int ... d^dr can be written as S_d int ... r^{d-1} dr, where S_d is the surface of a spherical shell of radius 1 in d dimensions. I leave out that S_d, as this does not affect the exponent. You can check this statement for d=2 (S_d = 2 pi) and 3 (S_d = 4 pi). Please react if this is not an answer to your question.
From the expression for the partition function you can immediately see that the deriv wrt h yields sum_i s_i. Beta=1/kT is incorporated into h. If you would miss an extra factor kT, that would not change the exponent.
Analyze how your system changes under "decimation" or a scale change, i.e. under the action of the the renormalization group. If you can do this accurately than you can estimate the critical exponents.
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It is one of the best lecture I have ever seen in the subject of RG. Thanks for the detailed and clear presentation.
Exactly!!!
Outstanding clearness. Thanks for the lecture!
De eerste helft is echt heel goed. Duidelijke motivatie --> conceptuele uitleg --> uitwerken van een voorbeeld.
would it be possible to rearrange your lectures?
if you put them in playlist, it would be much easier to know which lecture one has to watch first
thanks in advance
Thanks, this video really helped me to understand the renormalisation !
Great lecture!! --- NOW DO QUANTUM FIELD THEORY! :)
Very nice video introducing the subject. I struggled with it on scientific articles, but this has helped me a lot. I am very curious on model-specific solutions away from the critical point. I am curious if it can replicate the "sigmoidal"-esque behavior that many order parameters seem to show. I will watch the other videos on the subject!
Thank you. This video was very helpful.
Many thanks. This has been the clearest explanation of the renormalization techniques I have ever learned about. One question remains for me. Kadanoff (2000, p.238) says that "The existence of a phase transition requires an infinite system. No phase transitions occur in systems with a finite number of degrees of freedom." Can you please tell me how this fits into your discussion about the analysis of critical phase transition? (which minutes of your talk relate to this statement)? Huge thanks in advance, Olga.
Dear Olga, nice that you enjoy the video. For the answer to your question, I refer to my video on the Ising model, ruclips.net/video/hX_FrS5XO3I/видео.html, around minute 8.
thanks a lot
Prof Jos, In which video did you discuss critical exponents and at what time? BTW these are really fantastic lectures
Dear Somesh, thank you for your kind words. I think the best would be my video on the Ising model, see ruclips.net/video/hX_FrS5XO3I/видео.html Best regards, Jos
Thank you.
thank you
Thanks for the lecture! One question is how does different t^(k) couple?
Thanks for your question. The interaction between the t^k depends on the Hamiltonian of the s_i. It is not always easy to find it, but for the Ising model as in this case, it is assumed that the 'renormalised' interaction (between the t^k) only acts between nearest neighbours and then you can work it out, e.g. numerically. That is not the point of this movie. To see how such a procedure is carried out for the Ising model on a triangular lattice, see e.g. my video on real space renormalisation.
@@josthijssen6782 Thanks a lot! It’s really helpful!
Thanks for the detailed explanation. I have one confusion. In the derivation of the correlation function exponent, how do you get a factor r^(d-1) in the radial integral. Please explain
The integral int ... d^dr can be written as S_d int ... r^{d-1} dr, where S_d is the surface of a spherical shell of radius 1 in d dimensions. I leave out that S_d, as this does not affect the exponent. You can check this statement for d=2 (S_d = 2 pi) and 3 (S_d = 4 pi). Please react if this is not an answer to your question.
Thank you so very much Sir. Your youtube lectures are remarkably helpful to me particularly.
Great！
Why is there no beta dependence in the magnetic h part of the Hamiltonian in the partition function when finding the magnetization at 1:02:38 ?
From the expression for the partition function you can immediately see that the deriv wrt h yields sum_i s_i. Beta=1/kT is incorporated into h. If you would miss an extra factor kT, that would not change the exponent.
@@josthijssen6782 Ah okay, I didn't realize that beta was included inside of h, thank you 🙏
Is he the same guy who wrote the computational physics book?
I am afraid he is!
@@josthijssen6782 your book is really awesome. Helped me a lot.
Thanks.
@@adwaitnaravane5285 Thanks for your kind words.
Any chance you could share the notes in PDF or some other format? Thanks
Those are available on the Blackboard of TU Delft. I'm unsure of what the copyright rules are so I can't share it with you sadly.
Dear PM, you can find them on my github.com account. Repo name josthijssen/TabletNotes
Thanks! They are very helpful :)
how do we get the values of critical exponents??? what is the calculation?
Analyze how your system changes under "decimation" or a scale change, i.e. under the action of the the renormalization group. If you can do this accurately than you can estimate the critical exponents.
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