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- เผยแพร่เมื่อ 6 ก.พ. 2025
- (May 27, 2013) Leonard Susskind develops the Ising model of ferromagnetism to explain the mathematics of phase transitions. The one-dimensional Ising model does not exhibit phase transitions, but higher dimension models do.
Originally presented in the Stanford Continuing Studies Program.
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Continuing Studies Program:
csp.stanford.edu/
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Rehearsing the external magnetic field model; 1-dimensional Ising model 14:00; Duality 42:00; 2 dimensions Ising model 48:00; Mean field approximation 57:00; Adding an external magnetic field 1:20:00;
Thank you very much
always fascinating. Also fun to see what he's going to eat each day.
The connection with error correcting codes and information theory overall is amazing.
prof Leonard Susskind is the best physicist Contributed to
learn people physics in the world
Question from my side, at 54:46, it is not necessary that in D dimension, the number of neighbor particles are going to be 2*D. In case of D=2, you can create a lattice of squares (where neighbors=4), or of triangles (where neighbors=6), or hexagons (where neighbors=2) etc. and thus the similar thing can be possible for the higher dimensions.
Here the answer is going to vary as in the case of hexagon, (D=2, neighbor =2), one can't apply the error correction as there is going to be case of 50-50% probability too which is going to effect the fidelity.
The Ising model means a square/cubic lattice
@@Animations-mi1mc no, thats the square lattice Ising model, you can simulate ising model on any graph structure, not even a regular tiling, just replace the (2d) with the number of neighbor, and the mean field approximation probably breaks down
@@Animations-mi1mc No it doesn't. It means a spherical.
Thank you Stanford for posting this!
1:13:30 perfect explanation, in response to a question that just came out of the blue...!
its not really the dimension, its more about the graph structure on who is interacting with who
At around 1:08:22 professor talks about showing the slope of graph of the left handside of the equation depending on the temperature. Since "Y" is directly depends on the temperature, temperature can not be taken as a coefficient of this term. Any change in temperature will change "Y" value too. I hope Professor will make it clear for us.
1:04:27 I’m a bit confused here. So if I take a 1D lattice and say it couples equally to second nearest neighbors, then each spin has 4 neighbors. This is the same as the 2D Ising model (with first nearest neighbors). The 2D Ising model has a phase transition. But it seems to me that EVEN WITH second nearest neighbor couplings, the ‘telephone game’ argument works for the 1D lattice and so you should get No phase transition. As you go down the line it should decrease exponentially where the ‘probability of error in the message’ is just the probability that two neighbors in a row both happen to make a mistake.
Same with that argument at 1:15:00. That can be applied to 1D 2nd nearest neighbors implying no phase transition
1:32:31 bro "some distance epsilon" my guy is tweaking so hard
Ising solved the 1-D Ising model which showed no phase transition but mistakenly overgeneralized and postulated that higher dimensions would be the same. Onsager solved the much more complicated 2-D Ising model and showed phase transitions occur at dimensions higher than 1. Onsager won the Nobel prize in chemistry for his work but Ising's name is more known because the model is named after him. Would you rather be more well known but not win a Nobel or vice versa? I would take the former.
At 11:10, he says the average spin is tanh(Bj). I'm a bit unsure where he's getting that. Does anyone have an explanation? I would guess that the average spin should be 0.
Oh, nevermind! I understand it now.
It's since E=\mu \beta \sigma = -j \sigma. He's just solving for \sigma! D'oh!
MY CAR MECHANIC !!!
1:10:03 wouldn't it equal to 2(d)(J) divided by the boltzmann constant? because earlier he substituted T for 1/beta
Coefficients become irrelevant factors when it comes to relation of variables in the form of equation. Coefficients are there to make the dimension look good.
we don't care about boltzmann constant, we are not working with human scale temperature
hi. i am asian guy in korea. i enjoy this lecture so much, so i have took this lecture 4 to 5 in a day. But it tangled with my oriental pharmacy lecture, and it makes me hard to understand. Do u have any good way to study online lecture.
What is the probability that a standing wave does not have partical duality, do to the loss of velocity ?
19:26 He talks about correlation function.
J positive does NOT get rid of the symmetric solution at negative y ... I understand trying to simplify but symmetry of magnetization values at positive J is pretty fundamental. Lenny is being sloppy - but it doesn't take anything away for me. (Around when he is showing the graphical solution of the mean field approximation)
I followed completely till the 8th lecture but having some issues having an intuitive understanding since lecture 9- Magnetism. Are there any prereqs i should cover? Stat Mech is the first lecture series I'm doing.
At around 43:00 shouldn't the answer be (tanhBj)^n, not n-1?
they are counting the bond between tow particle.... since one spin is inducing another spin ...and so on...
You're right
The first derivation was for n spins, meaning that the first and the last were (n-1) links away but the one at 43:00 is for ith and (i+n)th spins which are also n links awayso the exponent should be n
yeap, you are right! it is because he starts with sigma_i not sigma_i+1
1:36:22 that’s not true. Just take T=0.5*T_c and look at the graph for B=0 then add a tiny B to shift the tanh curve ever so slightly. Then you still have 3 intersections
@Cristhian Asallam Sanchez Ramirez Actually everyone who cares about physics and aren't here for looking to see what Lenny "eats" cares. Idiot.
@Aeroscience, the graph is slightly misleading. In fact, only the right half of the σ-y plane is "physical", left half (negative y) just does not exist.
@@ptajimura what? negative y just mean spins down, thats the whole point of the second half of the lecture
thats exactly what i was thinking, they should have ask this instead of asking about the "epsilon" on the right hand side, does the tanh curve moves away fast enough for the straight line to not intersect it on the left hand side
I do not follow the argument that the mu1 mu2... are independent. They have a common spin, so how can they be independent?
+Robert Krutsch Then,how do you define your common spin?Here we just make a approximation,as Ising model is the approximation of Hersenberg model,unless you give the property of spin,or we just consider a simple situation,ignore the small effect temporarily,the most important thing is the result of Ising model approachs the result of the relevant experiment,it's enough for physicist,we still try to approach the experimental results,but before we doubt it,let's learn it step by step,these are just the lessons for high undergraduates.
I also have the same doubt, because if one of the mu's changes, then either the one before it or after it must change as well, right?
Yes
I think it is because mu2 is does not depend on whether sigma2 is up or down - mu2 is simply expressing the relationship between sigma2 and sigma3, and does not care whether this relationship would be from sigma2 = down to sigma3 = down, or sigma2 = up to sigma3 = up. (1*1 == -1*-1 == 1)
Even if you know sigma_2 you can't predict the value of mu_2, because it depends on both sigma_2 and sigma_3, and sigma_3 can be +1 or -1 with equal probabilities, so mu_2 can be +1 or -1 with equal probabilities even if you know sigma_2 (and you don't, actually).
the mean field approximation seems really.. unsatisfying
1:34
That's what she said.
There is a phase transition??
Hi. Can somebody told me how can I write a email to this teacher? I don't know him and I want to write something.
susskind@stanford.edu
23:50 - Actually it's 0.9801, not 0.981. We know 100*100 is 10000,. We subtract a row of 100 and a column of 100, but then we have to put one back, so 99^2 is 9801.
早くセクシー男優になって神でないことを証明したいです。
By the way, what happens if you change the sign on B, I.e if you shift the curve to thr RIGHT?
get the same thing but intersections are on the negative instead of the positive. ie. the orientation will just be the same but opposite sign.
hi i'm lila
Lila Gordon howdy lila
god these students are annoying
1:32:00 - This bit is ridiculous; that one student is just to aggressive and pushy. It shows extremely low respect for his peers; this stuff should be taken to office hours.
This is a continuing education class, they aren’t university student. They are encouraged to ask questions
@@aeroscience9834 Well, I think students in normal university classes should be encouraged to ask questions too; that's not what I'm taking note of. It's just that when one student asks a question, that's great for him, but it reduces the total amount of instruction time for all of the others. When the questions are dominated by one person, it feels like he's depriving the remainder of the class of some of the benefit they could have received, because he's having trouble keeping up. I still think he should get to have his questions answered, but at some point it feels like it would be more appropriate to do so outside of lecture time.
It's not at all the basic issue of questions - it's the extent and magnitude.
화^^
Fly
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Good god - this class has one of those students that doesn't have any respect for the other students. GO TO OFFICE HOURS - don't just assume that EVERYONE ELSE needs to hear your questions asked an answered. His inability to keep up is costing everyone else learning progress. So selfish.
This is continuing studies, they're not college students.
asking questions is not disrespecting other students. It helps to clear up the concept :).