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Piece of cheese


Mar
21
accepted Does $c = 0$ implies that the theory is “empty”?
Mar
11
awarded  Nice Question
Mar
7
comment Numerical Ising Model - Wolff algorithm and correlations
3. Since my first post, I put the system on periodic boundary conditions and I found a new value for the conformal weight of the spin operator: 0.05 . It still isn't the correct one (0.125) but it's on the "other side" as fixed boundary conditions had given me 0.4 . At least it tells me that boundary condition influence this derivation so we may on the right path, but I'm also not so sure of this calculation as it was only done over 5000 samples. I'll check that and maybe come back to you later. Again, I appreciate your input ;)
Mar
7
comment Numerical Ising Model - Wolff algorithm and correlations
2. Thank for the reference, actually I had already studied this book. Indeed they show how the autocorrelation time increases drastically at the critical point specially with single spin-flip (ie. Metropolis) "dynamics". That's why I'd like to make it work with the Wolff algorithm, I succeeded in calculating the right weight with the Metropolis algorithm (and free boundary conditions) but it took a lot of computation time and a more effective method will turn really useful in the next steps of my project.
Mar
7
comment Numerical Ising Model - Wolff algorithm and correlations
First, thank you for the input Srivatsan. To answer your questions: 1. Yes, the temperature is set to the critical value: I start with a totally random lattice (so $T = \infty$) and then I 'cool it down' using Wolff algorithm evolution with probability to add the neighboring state of $1 - \text{e}^{-2*K_c}$ where Kc is value close enough to $\frac{1}{T_c}$ for the correlation length at criticality being larger than my system size (I'm using lattices between 512x512 to 4096x4096 so 6-7 digits precision in the coupling).
Mar
5
comment Numerical Ising Model - Wolff algorithm and correlations
@Alexander: Thank you for the reference, I'll look into it. Otherwise, yes, since I opened this question, I put the lattice on a torus (periodic boundary conditions in both direction) and it gives totally different results but still incorrect. I went from $\Delta_{\sigma}$ = 0.4 to 0.05, the correct result being 0.125 . I'm also looking into that now.
Mar
5
comment Numerical Ising Model - Wolff algorithm and correlations
That's also what leads me to think that it has to do with the algorithm itself, and the information it uses when composing really large clusters such as the ones appearing at criticality.
Mar
5
comment Numerical Ising Model - Wolff algorithm and correlations
@CarlWitthoft : I really don't think it's the implementation: I first did it on my own and double,triple, etc... checked it; then I copied a version from the internet ( physics.buffalo.edu/phy411-506-2004/Topic3/topic3-lec7.pdf ) and it still isn't working (at the level of giving good correlations).
Mar
5
asked Numerical Ising Model - Wolff algorithm and correlations
Feb
27
accepted Normal ordering of the identity operator
Feb
26
asked Normal ordering of the identity operator
Feb
17
asked Does $c = 0$ implies that the theory is “empty”?
Feb
12
asked Infinite heat capacity or susceptibility means fluctuation on all scales
Dec
14
awarded  Yearling
Dec
12
awarded  Popular Question
Jun
1
comment 1 dimensional Ising model
@Vibert Thank you for the precision and for pointing my misunderstanding. Is there also in $D\neq 2$ "graphical duality" I mean a direct graphical link between the loops of the high and low K expansion? And not just the algebraic equality between the partition functions.
Jun
1
answered 1 dimensional Ising model
May
26
comment Strain and stress tensor
Symmetry of $\epsilon$ comes from its definition, symmetry of $\sigma$ comes from the absence of internal torque.
May
24
accepted Is there a “covariant derivative” for conformal transformation?
May
24
accepted Zero point fluctuation of an harmonic oscillator