@DanielSank Nice. This is something in a similar vein:

I don't know if you saw it already and/or you (dis)like it, but I found it to be one of the most meaningful short videos :)

@Semiclassical You around?

I had some questions related to the Ising model and spin glass systems

We know for spin systems the energy function is of the form $$E(\Bbb x;\mathrm J) = -\frac{1}{2}\sum_{m,n}J_{mn}x_mx_n-\sum_{n}h_nx_n$$

The actual probability distribution would be of the form:

$$P(\mathbf{x}|\beta,\mathbf{J})=\frac{1}{Z(\beta,\mathbf{J})}\text{exp}[-\beta E(\mathbf{x;J})]$$

where $Z(\beta,\mathbf{J}$ is the normalization constant (partition function) expressed as $\sum_{x}\text{exp}[-\beta E(\mathbf{x;J})]$

To clarify $\mathbf{x}$ is a vector containing spin states ($\in\{+1,-1\}$) of all the individual "particles" (don't know if that's the right term)

$\mathbf{J}$ is probably a matrix containing all the couplings any between two "particles" with spin

$\beta$ is the inverse temperature i.e. $\frac{1}{k_B T}$

I am not completely sure how this partition function and probability distribution is derived but I expect it would be along the similar lines of what we do for canonical ensembles in statistical mechanics

Anyhow, that was not the main part

They say that the following quantities are "impossible" to evaluate (using the probability distribution $P(\mathbf{x}|\beta;\mathbf{J})$):

$$\langle E\rangle_P = \frac{1}{Z}\sum_x E(\mathbf{x;J})\text{exp}(-\beta E(\mathbf{x;J}))$$

$$S=\sum_x P(\mathbf{x}|\beta,\mathbf{J})\ln\frac{1}{P(\mathbf{x}|\beta,\mathbf{J})}$$

I'm not sure whether they mean "literally impossible" or just difficult to evaluate. I don't see any reason why they should be "impossible" to evaluate.

They go on to "approximate" $P$ using another "separable" (also not exactly sure what they mean by that) distribution $Q(\mathbf{x;a})$

$$Q(\mathbf{x;a})=\frac{1}{Z_Q}\text{exp}(\sum_n a_n x_n)$$

To measure the quality of approximation we introduce a free energy:

$$\beta \tilde F(\theta) = \sum_x Q(x;\theta) \ln \frac{Q(x;\theta)}{\text{exp}[-\beta E (\mathbf{x,J})]}$$

which can be simplified to $\beta\langle E(\mathbf{x;J})\rangle_Q - S_Q$ (setting $k_B$ to $1$ in definition of $S$)

Alternatively, it can also be simplified to $D_{KL}(Q||P)+\beta F$ where $\beta F = -\ln Z(\beta,\mathbf{J})$

$F$ sounds like some version of "Helmholtz free energy"

$D_{KL}(Q||P)$ is the relative entropy between approximate distribution $Q(\mathbf{x},\theta)$ and real distribution $P(\mathbf{x}|\beta,\mathbf{J})$

The goal is to vary $\theta$ so that $P$ is best approximated

@gateprep ?

Ugh, my question is becoming a lengthy monologue now

Ask in the Problem Solving room

I'm not really feeling like attempting a mechanics problem now

Also, I'm at work now

@gateprep Seems to be solved here. Didn't see their solution though.

You really need to learn to use Google first.

Or if you're concerned about privacy use DuckDuckGo :P

@Semiclassical Anyhow, one of my main confusions was where they're getting the probability of a particle being in the +1 spin state to be $\frac{e^{a_n}}{e^{a_n}+e^{-a_n}}$. Couldn't locate that derivation in the Ising model's wiki page

@DanielSank Oops, I actually re-posted the same speech by Feynman which ACM was talking about (and which you replied to). Didn't notice that earlier. Sorry for that redundant ping :P

@Slereah morning!

Lol, after a long time here's an actually interesting Meta post ^

@JohnRennie The real questions are: 1) Whether IT is a "last resort" since they the physics job market is quite bad (as knzhou suggets) 2) Do people get bored of working in physics (as a professional theorist or experimentalist), after a while? 3) Or are there some other reasons?

At least 3 of the theorists I know (including ACM) seem to be happier working in software development rather than physics theory

That sure indicates a certain level of boredom (?)

Or maybe I'm biased because all 3 of them either work in string theory or mathematical physics

@Slereah IT work also has lots of parts/types I guess? I thought some are interesting...like machine learning jobs

I dunno enough about such jobs tho

Ah, true. Most of them apply existing algos, yeah

Sounds boring

I worked for a couple of weeks for a startup...I sort of enjoyed that because we were attacking some very new types of problems (albeit using existing algorithms) ... like predicting food production and distribution rates in different parts of the country, and finding development index, etc. However, now that I look back I probably wouldn't enjoy that if it were longer period of time

It was mostly enjoyable coz I got to learn the data science frameworks and stuff

@JohnRennie Exactly!

It's really fun when you have some novel problems to attack

Rather than the boring clerk work

Like web development stuff

@JohnRennie Someone told me that's one of the good reasons for working in startups/small companies is that they are better for self-development and are much more enjoyable than working in a huge company where you are a small fish. In small companies you can make much more impact and also get to learn a lot since you have to do a variety of work yourself. I don't know how much that is true, but sounds about right

@Slereah Well, doesn't matter as long as they're profitable enough and they're feeding me well :P

Ah, the job security part is a thing, yes

If the startups fail, they'll kick you off

:P

@JohnRennie Ah, but I guess people with less than ~10 years of experience wouldn't classify as "experienced"?

I heard CERN doesn't pay well

"people that dedicated to science don't care about money"

Lol, you don't know the number of people who leave their jobs at CERN

Every year

There was some statistics released somewhere

@AvnishKabaj I love science and everything, but wouldn't really want to settle for something that doesn't pay me sufficiently for what my skills are worth. And tbh, to become a physicist or mathematician you need to learn several times more than the average programmer.

@AvnishKabaj What is not?

@AvnishKabaj That's some nonsense philosophy that you can't achieve your dreams without sacrificing the monetary side. I don't agree with it

@AvnishKabaj You could build something of your own (make your own company, etc.) and collaborate with CERN rather than working for them

Also, I feel currently science is extremely under-funded. We really need more people like Elon Musk (although he is more of an engineer) to take the lead, so that governments start injecting more into science than military.

With quantum computing and data science and stuff, good times ahead

@AvnishKabaj Sure, but he's a good leader.

With a sufficiently strong enthusiasm to drive people forward

People need hope

He gives them that

You'll need a landing spot :P

Rooftop?

@CooperCape It's become synonymous ;)

Trump isn't a bad role model either :P

You need to be a "Trump of science"

What's he upto, nowadays?

Apart from his ever-pending meet with his bro

lol

I should join twitter it seems

pravduh"?

Good idea imo XD

We especially need something like that here in India

People's vote would be the best way to go...

Online voting

(At least if you some way to make it secure)

point^

@Mithrandir24601 Yeah, but I can't think of any better metric. At least ones which lots of people think are not credible will get eliminated.

But then again, lots of people also seem to be content with fake news...

@Sid ?!?@#O

That's some real news

lolol

awesome

Well, I mean if you're given a choice between the two, Trump made the right one

:P

Commenting on that will get me banned XD

I like his big broad grins tho

And his shiny face

bbc.com/news/world-asia-44351807

@Sid Oh of course, how could I miss that!

Absolutely adorable

@DawoodibnKareem Starting any nuke war would imply destroying themselves too...so I doubt Iran would support that....

@DawoodibnKareem Except for NK

They can do anything

Including self-destruction

Kim would just go and settle somewhere else

Howard Stark's philosophy actually makes sense now, yeah

@Albas They tend to be well-rounded ;)

@CooperCape What's the highest and lowest possible grades?

Is there like A***?

Ah, and by chance something goes wrong and you get A in math or physics, you won't be admitted?

I see. Good luck then :P

Tough days for you

@CooperCape Congrats for physics, then :)

Math is still remaining!

@DawoodibnKareem People like to believe that cigarettes won't kill them.

While that doesn't apply to nuclear weapons.

Also, one is instantaneous, while the other isn't

@CooperCape Gosh...how many physics papers