Recent content by Tilde90

Thanks for your answer, mfb. Are you sure about what you say? The fact is that the right-hand side of the Ampere's law is different between the free space and the auxiliary material, and it is equal to zero in the latter. So the only source of the magnetic field in the material would be the...

Let us consider the following thought experiment. There is a magnetic field in free space produced by a steady current, hence solution of the (magnetostatic) Ampere's law Curl H = J. There is also a material with some parameters ε and μ and no currents, where the Ampere's law is Curl H = 0...

Thank you! This makes perfectly sense. Just a question: with order parameter you mean the temperature, right? EDIT: The order parameter in the Ising model is the magnetization itself, which is different from zero in the ordered phase (and viceversa).

Apparently, with \alpha=0 it is implied for the specific heat to diverge logarithmically, i.e. \sim -\log(1-T/T_c). Hence, I guess that we can consider the heat capacity as another expression of the second phase transition, being the specific heat a second derivative of the free energy. Now...

I didn't consider that heat capacity is actually a second derivative of Helmholtz free energy F. Anyway, my question remains: has the 2D/3D Ising model a second order phase transition for both the susceptibility and the specific heat? And is there a first order phase transition when considering...

Considering d=2 or d=3, the Ising model exhibits a second order phase transition at the critical temperature T_c, where the system goes from an ordered phase (spins preferably aligned in a certain direction) to a disordered one. This is reflected by the behaviour of the susceptibility, similar...

Isn't there anybody who knows something about Quantum Monte Carlo methods? :)

Hi, I understood the formal derivation of various QMC methods like Path Integral Monte Carlo. However, at the end of the day I still have a doubt on how to effectively use these techniques. Given that we can interpret \beta in the quantum operator e^{-\beta\hat{H}} both as an inverse...

Sure. It's an Italian paper, http://www.dcci.unipi.it/~ivo/didattica/dispense.chimteo/secquant.pdf , pages 11-13 (and following pages for two particle Hamiltonians). The formalism is very clear.

Thank you all for your replies. I apologise for the lack of details in my first post, but that evening I was at the brink of desperation trying to prove that result. :-) Finally, I found a proof online, but as you say it's not something which books usually demonstrate (despite its importance).

Please, can somebody show me why a Hamiltonian like \sum_nh(x_n) can be written as \sum_{i,j}t_{i,j}a^+_ia_j, with t_{i,j}=\int f^*_i(x)h(x)f_j(x)dx? Thank you.

Thank you for your help, Stephen. Following your link, I found this page (http://en.wikipedia.org/wiki/Sample_covariance_matrix#Sample_mean_and_covariance): the third equation, written again with vector formalism, proves my supposition, apart from the denominator, which is (m-1) as you...

Thank you Stephen for your answer. I will try to make my point clear. My problem is with the command "cov" in MATLAB, which allows a user to obtain a covariance matrix given a sample matrix of observations and variables. According to the documentation...

Suppose we have a mxn matrix, where each row is an observation and each column is a variable. The (i,j)-element of its covariance matrix is \mathrm{E}\begin{bmatrix}(\vec{X_i} - \vec{\mu_i})^t*(\vec{X_j} - \vec{\mu_j})\end{bmatrix}, where \vec{X_i} is the column vector corresponding to a...

Thank you very much chiro. I mistakenly believed that the "stochastic" integral were easier to calculate, as in the demonstration of the exact solution of the GBM with Ito's lemma it seems that they just integrate both terms of the SDE dlogX_t=(\mu-\frac{\sigma^2}{2})dt+\sigma dW_t.