| ... | @@ -49,7 +49,7 @@ For more info, see [arXiv:1008.3933](https://arxiv.org/abs/1008.3933). |
... | @@ -49,7 +49,7 @@ For more info, see [arXiv:1008.3933](https://arxiv.org/abs/1008.3933). |
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```
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```
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The effective coupling constant is computed according to the prescription:
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The effective coupling constant is computed according to the prescription:
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```math
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```math
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\dfrac{1}{g_{\textrm{eff}}}=\dfrac{1}{g_0} - \dfrac{m}{2\alpha_+}\dfrac{K}{2\hbar^2\pi^2 dx},
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\dfrac{1}{g_{\textrm{eff}}}=\dfrac{1}{g_0} - \dfrac{m}{2\alpha_+}\dfrac{K}{2\hbar^2\pi dx},
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```
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```
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where $`K=2.442 75`$ is a numerical constant. In this formula, we assume that all states contribute to the densities. Physically, it means that we take into account states up to the maximal value of energy set by the lattice, which is of the order $`E_c\approx 3\frac{\hbar^2\pi^2}{2mdx^2}`$ (assuming that $`dx=dy=dz`$).
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where $`K=2.442 75`$ is a numerical constant. In this formula, we assume that all states contribute to the densities. Physically, it means that we take into account states up to the maximal value of energy set by the lattice, which is of the order $`E_c\approx 3\frac{\hbar^2\pi^2}{2mdx^2}`$ (assuming that $`dx=dy=dz`$).
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*Note*: when working with this renormalization scheme value of tag `ec` will be ignored.
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*Note*: when working with this renormalization scheme value of tag `ec` will be ignored.
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