Homework 2: Ising Model

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Good luck

Prova prova

Hi Dr Civelli

some first questions:
1- may you give us the formula for the specific heat (for those who do not have the book) : SMAC p. 235 and the expected values table 5.3 page 236 ?

2- even after having imported random python does not recognize the name "ran" (last line of the first algorithm)

thank you Sir

1-
https://drive.google.com/file/d/1vIcFejx4twDSm30-24GuZSIvwneVwYk4/view?usp=sharing

2-
True, but you know what you have to replace "ran" with, right? This is part of the exercise.

Ok, Thanks !

Hand-in your Homework 2 by this Friday at 13h45. Send your report to marcello.civelli@u-psud.fr. We require your file in the html format, in order to avoid possible compatibility issues. In particular all the outputs (figures and numbers) should be well displayed. Write the name of your file in the form yourname_lastname.html. Any issue, let us know asap.
Marcello

Hi,

I was asking myself: the specific heat is also defined as de/dT: it is also coherent with the graphs we get. So why did we prefer using the SMAC definition with the variance, is there a computational reason to not take a discrete derivative?

You may do as you say, but you need to build a well refined grid of points energy as a function of temperature to do a good numerical derivative (or trick with some interpolation scheme). This assuming also that the statistical fluctuation of each point E(T) is well controlled (i.e. error bars are small for each T). So it is a priori more work and a step more of approximation. In general it is easier to use the variance formula.

Hi Dr Civelli,

you ask " For large lattices, such as $32\times 32$, determine numerically the mean cluster size flipped at each step as a function of temperature." At what steps you want the curves ?

Thanks

I want curves of the cluster-size distribution for different temperatures (so few representative graphs). This is stated by "Plot histograms of the distribution of cluster sizes. Explain the behavior that you observe, especially, considering temperatures T<<Tc, T∼Tc and T>>Tc. " and this after the sentence that you mention (that says what you should calculate rather than what you should plot)

OK, I thought it was another question; thank you

Dear Dr. Civelli,

for the local Metropolis approach, should a sample of the Energy be taken after each attempt to flip a spin (and therefore in the inner loop) or in the outer loop, hence after each "sweep-step"?
Thank you in advance

In a MC algorithm one has to read the energy (or any other observable) of any allowed configuration that is visited....then you can infer when you have to do it.....