Statistical Mechanics Lecture 9

(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.

Stanford University:

Continuing Studies Program:

Stanford University Channel on YouTube:

[glendeloid]

always fascinating.  Also fun to see what he's going to eat each day.

[joabrosenberg]

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;

[jaimelima]

The connection with error correcting codes and information theory overall is amazing.

[alamri]

prof Leonard Susskind is the best physicist Contributed to
learn people physics in the world

[prasoonvishwakarma]

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.

[qbtc]

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.

[jimmyb]

1:13:30 perfect explanation, in response to a question that just came out of the blue...!

[jacobgreen]

1:32:31 bro "some distance epsilon" my guy is tweaking so hard

[npw]

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.

[hasanunlu]

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.

[verystablegenius]

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)

[aeroscience]

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.

[samardev]

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.

[rupayansaha]

19:26 He talks about correlation function.

[calebpoemoceah]

What is the probability that a standing wave does not have partical duality, do to the loss of velocity ?

[jacobgreen]

1:10:03 wouldn't it equal to 2(d)(J) divided by the boltzmann constant? because earlier he substituted T for 1/beta

[blanamaxima]

I do not follow the argument that the mu1 mu2... are independent. They have a common spin, so how can they be independent?

[kevinhevans]

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.

[aeroscience]

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

[frankjohnson]

At around 43:00 shouldn't the answer be (tanhBj)^n, not n-1?