Statistical phyics Definition and 6 Discussions

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1. Einstein solid state model exercise

I tried to solve it considering the canonical ensemble (since the system is at the equilibrium with temperature T) and started finding the partition function: The problem is I am not sure if I have done it correctly and need help because I don't really know where to check.
2. Ising model autocorrelation function calculation

Dear Mr. and Ms., I am trying to measure the autocorrelation functions of 2D ising model based on the equation given by where A(t) denote a measure. I calculate a c(t) of magnetization. I calculated in this way data_path = f"../../trajectory/data.txt" data = np.loadtxt(data_path)...
3. I Demonstration of inequality between 2 variance expressions

Just to remind, ##C_\ell## is the variance of random variables ##a_{\ell m}## following a Gaussian PDF (in spherical harmonics of Legendre) : ##C_{\ell}=\left\langle a_{l m}^{2}\right\rangle=\frac{1}{2 \ell+1} \sum_{m=-\ell}^{\ell} a_{\ell m}^{2}=\operatorname{Var}\left(a_{l m}\right)## 1)...
4. I Can we consider this system as an Einstein model of a Solid?

Hello Everyone! I am interested in examining the case of an isolated Einstein Solid (ES) with a decreasing number of oscillators. The total amount of energy of the ES is considered fixed. Whenever an oscillator abandons our model, it "leaves behind" the amount of energy it contained, so that the...
5. I Changing Summation to Integral

This is the text from Reif Statistical mechanics. In the screenshot he changes the summation to integral(Eq. 1.5.17) by saying that they are approximately continuous values. However,I don't see how. Can anyone justify this change?
6. Thermodynamic identities

Homework Statement Let x, y and z satisfy the state function ##f(x, y, z) = 0## and let ##w## be a function of only two of these variables. Show the following identities: \left(\frac{\partial x}{\partial y}\right )_w \left(\frac{\partial y}{\partial z}\right )_w =\left(\frac{\partial...