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seen Jul 15 at 16:36

Piece of cheese


Jul
8
comment Numerical Ising Model - Wolff algorithm and correlations
depending on the energy shift from breaking links to the boundary and with fixed boundaries a lot of rejection occurs), but with free boundaries, a low T starting point is roughly 4 times faster.
Jul
8
comment Numerical Ising Model - Wolff algorithm and correlations
Interesting, I have a different way of reaching equilibrium I would first monitor the value of the mean energy per spin (for each configuration) and read from there how many steps I needs for each systems size (I usually stick to 3,4 sizes also). I did check if starting from a totally ordered configuration is quicker than a totally disordered, and well amusingly it depends on the boundary conditions: with fixed boundaries, disordered is very very advantageous (the reason it that the Wolff algorithm needs to be modified with fixed boundaries with an accepting factor 'à la Metropolis'
Jul
7
comment Numerical Ising Model - Wolff algorithm and correlations
Thank you very much for the input, I will look deeper at your code. Can I ask you how many systems did you simulate (ie. are you averaging on) ? I managed to derive a good coefficient in my case too (very close to 0.249 ) but my data was noisier, probably the sum used to fit (linearly in log-log scale) cancelled most of the noise. Also how many Wolff evolution steps do you perform to thermalize starting from ordered T = 0 configurations? Many thanks again ;)
Jul
7
accepted Numerical Ising Model - Wolff algorithm and correlations
Jul
4
accepted What is a 'height field'?
Jul
4
comment What's the critical temperature of the XY model on a triangular lattice
Yes, indeed they do locate the critical temperature using the 4th Binder cumulant, though my simulations are giving me different results on the x and y axis, I definitely need to look deeper into that. Many thanks ;)
Jul
4
accepted What's the critical temperature of the XY model on a triangular lattice
Jul
3
asked What's the critical temperature of the XY model on a triangular lattice
Jul
2
comment Critical temperature difference between Ising and XY model
Right, makes sense!
Jul
2
awarded  Curious
Jul
2
comment Critical temperature difference between Ising and XY model
Ok, but so is it a coincidence that the Ising model has same critical coupling for spins and loops or is there some kind of 'self-duality' behind?
Jul
1
comment Critical temperature difference between Ising and XY model
ps: In the Ising case, I managed to very precisely check the critical coupling value given by the formula above. That's why it's even more puzzling for me.
Jul
1
comment Critical temperature difference between Ising and XY model
Ok, it's an high-T approximation of the O(n) spin model? Is it still correct near the critical temperature? It may explain why my O(2) Monte-Carlo simulations (on triangular lattice) are giving me a critical coupling around 0.58 . I haven't been able to find a reference with the right value of the critical coupling on triangular lattice. Would you know of one too? Many thanks for all the help you already gave me.
Jun
30
comment Critical temperature difference between Ising and XY model
@YvanVelenik: Thanks for confirming my intuition, I'll look more into this inequality. Sorry if it's a foolish question: what's the difference between the spin and the loop models? Aren't the loops just the boundaries between the different spin clusters?
Jun
28
asked Critical temperature difference between Ising and XY model
Jun
23
asked What is a 'height field'?
Jun
13
comment Monte-Carlo and $O(n)$ models for non-integer n
@amlrg: Hi, thank you for the references, I'm still reading them (and the references within) but I can already tell you that it helped me making a few steps forward. I'd give you the bounty but your answers needs to be in a proper answer post for that and not an underlining comment. Please do so, so I can reward you ;)
May
19
answered Monte-Carlo and $O(n)$ models for non-integer n
May
2
asked Monte-Carlo and $O(n)$ models for non-integer n
Apr
21
comment What is the connection between Conformal Field Theory and Renormalization group in QFT?
Well it seems that you have all pretty much figured out: conformal field theories are a subset of quantum field theories corresponding to the point(s) at which the beta function vanishes. It may seem not much interesting to look at subset of 'vanishing measure' in the space of quantum field theories but actually: conformal symmetry is a really strong constraint and is enough to solve exactly some theories in 2d, and you can derive results near critical points from the so called conformal perturbation theory. The main references are Ginsparg lecture notes (arXiv) and thee book by DiFran & al.