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Madder

 Mathematics

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Madder
yst 07:04
i was under the impression, that a tuple is a finite ordering (a,b,c,d)
but we usually refer to tensors as tuples (t_ijkl)
even though no ordering seems to be given?
 

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General chat for Physics SE (physics.stackexchange.com). For M...
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Madder
Wed 10:11
Hello i have exactly the same request as this person
https://math.stackexchange.com/questions/3451152/reference-for-onsager-s-solution-of-the-2d-ising-model

and i am not finding any resources that explain the original solution as it was presented
Madder
Feb 10 08:25
ideas? chat.stackexchange.com/transcript/message/67186428#67186428
Madder
Feb 9 22:12
Usually if you look up components of universe you find energy , matter, dark energy, dark matter, excluding the dark stuff, can we just equate energy and matter and call everything inside the universe "matter"
Madder
Feb 9 22:12
If energy and matter are equivelent, is this statement logically correct?
" The stuff in the universe is called Matter" or " the universe is made out of spacetime + matter"
Madder
Feb 9 22:11
Hello, a little bit of a fun question
Madder
Jan 11 20:48
for now.... :) Chat gpt already is very helpful and sees some stuff i miss. and it is not even a real AI
Madder
Jan 11 20:06
I was thinking this today. I am truly previliged to study physics in this age. I can save so much time just googling... its crazy, but the natural progression of mankind. At one point, we will cease to study physics, because we will deligate this objective to an AI and download information throught agumentations !
Madder
Jan 11 19:15
does it make sense to you guys that the eigenvalues are to the power m instead of $m/2$? i have looked at two different books and they wrote it like this. It is regarding the partition function of ising model.
Madder
Jan 11 19:14
user image
Madder
Jan 6 13:18
This is taken from the "Baxter: Exact solvable models in statistical physdics"
all the information one need is in the image, how he is reaching htat result idk. i tried to do the math, but it just does not compue
Madder
Jan 6 13:18
user image
Madder
Jan 3 08:13
@JohnRennie So it is part of the definiton?
Madder
Jan 3 08:03
@JohnRennie Hello John. Thank you for your answer. Not really. I have made the mistake of refering to a lattice point as an atom, which you pointed out. The crux of the question however remains to be understood, if this is an implication from the definition, or a part of it.
Madder
Jan 2 13:48
Def: Primitive Unit-cell: a region that fills the point space without any overlapping when translated through any translation vector T
Note: You can write the translation vectors as infinite set of tripplets (In case n=3) this avoids also the order of the translation since (2,1,0) does not care if you go 2 steps x then 1 y or vica verca)
You guys fine with this argument?
Madder
Jan 2 13:48
if anyone is interested...
Madder
Jan 2 13:48
i solved my problem...
Madder
Jan 2 13:20
anyone has a comment regarding chat.stackexchange.com/transcript/message/66919085#66919085?
Madder
Jan 2 12:28
@naturallyInconsistent what :D ahhahahha oh i get it now
Madder
Jan 2 12:24
these definitions are very unclear. So a unit cell need to reporduce the lattice by translation of the vector $T=ax+by+cz$ for some unit vectors and constants. But does it mean i fix one vector and keep translating along side? well i will not cover whole space!
If i translate along ALL the vectors, i will get double regions! and thus break my "no overlap" rule
EG: square lattice. 2x+y translation will put the square shape of my unit cell in that area, then i will have to do with 2y+x combination, but this is the same, and i will draw it double! breaking my no overlap rule...
Madder
Jan 2 11:21
why it is necessary? because i thought that was the definition. I am guessing it is not.
i do not understand the boundary thing you mentioned.
Madder
Jan 2 10:42
Or is it such, that the unit vectors, span one possible primitive unit cell among many primitive unit cells? and not every primitive unit cell has vectors spanning it (as triple product)
Madder
Jan 2 10:25
You often find in books examples of unit cells, and sometimes they give squiggly lined unit cells to show none uniqueness. EG: Aschcroft. But the problem i see is, the primitive unit vectors are not able to produce such shapes. So how can they be considered primitive unit cells?
Madder
Dec 30, 2024 16:13
i will check it out. Thanks!
Madder
Dec 30, 2024 16:11
Thank you for your patience @SillyGoose @ACuriousMind
Madder
Dec 30, 2024 16:11
That makes so much sense. and i believe it was the missing puzzle.
Madder
Dec 30, 2024 16:07
It is dealing with the canonical ensemble.
Madder
Dec 30, 2024 16:07
Or is it because the temperature itself is a statistical value, which can only be given as an average ? and thus have "fluctutation"
Madder
Dec 30, 2024 16:05
And the cause of these fluctations is, statistical nature, because it is really not known if the system is at $E_o$?
Madder
Dec 30, 2024 16:02
I do not know why i cant get over this, but wikipedia defines:
In statistical mechanics, thermal fluctuations are random deviations of an atomic system from its average state.
and once you pick a state, you are throwing these statistical definitions out of the window.
Madder
Dec 30, 2024 16:01
Is there any way i can understand the statement they are making in other formulation or words that is more intutive? i am still very confused about the "thermal fluctation" part.
Madder
Dec 30, 2024 15:58
do you advice a particularly good and intutive source on understanding these nuances in statistical mechanics? it seems my foundation is terrible..
Madder
Dec 30, 2024 15:55
So there is evolution even after you specify the microstate (in the case of this model). It is somehow more visual in the gas case because i can see the particles moving due to newtonian laws, i just did not consider some dynamic due to he hamiltonian of the model.. so i guess the answer is "no" its not frozen in time even if T= cst
Madder
Dec 30, 2024 15:54
@ACuriousMind Ok this is very interesting because i honestly thought nothing would happen.
Madder
Dec 30, 2024 15:53
@SillyGoose yes. but again, we only look at classical case here. no Schrödinger equation.
Madder
Dec 30, 2024 15:52
@ACuriousMind Does having hamiltonian mean directly= system dynamics?
Madder
Dec 30, 2024 15:52
Somehow i am having even more questions as this conversation continues, which shows the depths of my ignorance lol.
Madder
Dec 30, 2024 15:50
Yes for example for gas particles they will move provided by newtonian mechanics, but this model has no dynamics?
Madder
Dec 30, 2024 15:48
the partition function is there to give me the probability of the system being in a state because i do not know, right?

but when i KNOW, then Z is useless , okay!
This means the system is frozen in time. correct?
And there is no use of speaking about temperature, because it is statistical.
Madder
Dec 30, 2024 15:47
i think my misconception comes from not understanding these elementary definitions.
Madder
Dec 30, 2024 15:45
@ACuriousMind The temperature comes into play when you insert the hamiltonian into the partition Function. it is given by $\beta$
Madder
Dec 30, 2024 15:43
I just want to understand something crucial for the chain of thought in my brain.
if i take any snapshot of the system to be in a microstate and spesicy it to be exactly $s$ ie i know the configuration as a whole. And T = constant. Does this change with time?
What happens if T is now changing, does the snapshot change ? or do these questions make no sense?
Madder
Dec 30, 2024 15:40
We are viewing it from a classical point of view.
Madder
Dec 30, 2024 15:37
Maybe you can answer me this, because i might have minsconception about microstates.
if i pick a microstate in this frame, it will not evolve with time?
will it evolve with Temperature?
Madder
Dec 30, 2024 15:35
https://i.sstatic.net/jtY3A8eF.png
Book by An Introduction to Exactly Solved Statistical models -- Giuseppe Mussardo
Madder
Dec 30, 2024 15:34
Because the authors are doing it?
Madder
Dec 30, 2024 15:33
But generally speaking, you can consider a system where you can take 1 or 0 in each point and you have a grid of NxN points. And a microstate is when you know the values. pointing up means =1
Madder
Dec 30, 2024 15:32
Well it is a niche-topic that you might not be familiar with. here is the exact quote:

"Let’s consider the two-dimensional Ising model at low temperatures and suppose that
it is in the state of minimal energy in which all the spins have values +1. The thermal
fluctuations create domains in which there are spin flips, such as the domain in fig..."
Madder
Dec 30, 2024 15:31
@SillyGoose Oh yes i am.
Madder
Dec 30, 2024 15:30
@SillyGoose What do you mean by Source? Like a heat bath?