Timeline for Sums of Ising Variables
Current License: CC BY-SA 3.0
9 events
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| Apr 5, 2018 at 5:49 | comment | added | Yvan Velenik | The term you are interested in will scale linearly with the number of spins in the system. The exact constant is probably impossible to determine, except in dimensions $1$ and $2$. Note, however, that $\langle H^2\rangle$ scales as the square of the number of spins, so the term you are interested in contributes negligibly to this expectation. | |
| Apr 5, 2018 at 5:25 | comment | added | P. C. Spaniel | Thanks! I edited to add a small new question, if you have any clue on how to compute that particular mean value that would be great! thanks! | |
| Apr 5, 2018 at 5:24 | history | edited | P. C. Spaniel | CC BY-SA 3.0 |
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| Apr 4, 2018 at 14:58 | history | edited | P. C. Spaniel | CC BY-SA 3.0 |
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| Apr 4, 2018 at 14:57 | comment | added | Yvan Velenik | OK, then all the expectations $\langle \sigma_i\sigma_j\sigma_k\sigma_l\rangle$ are strictly positive (as long as $\beta>0$). This follows, for example, from the GKS correlation inequalities. The latter imply that $\langle\sigma_i\sigma_j\sigma_k\sigma_l\rangle \geq \langle\sigma_i\sigma_j\rangle \langle\sigma_k\sigma_l\rangle$. Now, for any $i,j$ neighbors, $\langle\sigma_i\sigma_j\rangle \geq \tanh(\beta J) > 0$ for all $\beta>0$. | |
| Apr 4, 2018 at 14:46 | comment | added | P. C. Spaniel | you are right! Sorry for the misunderstunding, I meant that the mean value is zero. Let me edit. | |
| Apr 4, 2018 at 7:12 | comment | added | Yvan Velenik | I don't understand the question. What do you mean by "this term is zero"? Each term is a function of the spin configuration, not a number... | |
| Apr 4, 2018 at 1:34 | history | edited | P. C. Spaniel | CC BY-SA 3.0 |
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| Apr 4, 2018 at 1:17 | history | asked | P. C. Spaniel | CC BY-SA 3.0 |