물리:드알메이다-사울레스_선

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물리:드알메이다-사울레스_선 [2026/09/27 16:38] – [감수율] admin물리:드알메이다-사울레스_선 [2026/09/27 16:49] (current) – [감수율] admin
Line 169: Line 169:
 \sum_i \langle S_i^\alpha S_i^\beta S_i^\gamma S_i^\delta \rangle  &=& \lim_{n\to 0} \frac{\partial^2}{\partial \Delta_{\alpha\beta} \partial \Delta_{\gamma\delta}} \left[ Z^n \right]. \sum_i \langle S_i^\alpha S_i^\beta S_i^\gamma S_i^\delta \rangle  &=& \lim_{n\to 0} \frac{\partial^2}{\partial \Delta_{\alpha\beta} \partial \Delta_{\gamma\delta}} \left[ Z^n \right].
 \end{eqnarray*} \end{eqnarray*}
 +[[물리:복제_트릭|복제 트릭]]에서 했던 것처럼 [[수학:허바드-스트라토노비치_변환|허바드-스트라토노비치 변환]]을 수행하면
 +\begin{equation}
 +    \left[ Z^n \right] ~=~ \exp \left( \frac{N \beta^2 J^2 n}{4} \right) \int \prod_{\alpha < \beta} dq_{\alpha \beta}
 +    \exp \left( -\frac{N \beta^2 J^2}{2} \sum_{\alpha < \beta} q_{\alpha \beta}^2 \right)  \exp \left( N\ln \text{Tr}^{\prime} e^{L} \right).
 +\end{equation}
 +\begin{align}
 +    L \equiv \beta^2 J^2 \sum_{\alpha < \beta} q_{\alpha \beta} S^{\alpha} S^{\beta}
 +\end{align}
 +
 +
 ======참고문헌====== ======참고문헌======
   *H. Nishimori, //Statistical physics of spin glasses and information processing an introduction// (Clarendon, Oxford, 2001).   *H. Nishimori, //Statistical physics of spin glasses and information processing an introduction// (Clarendon, Oxford, 2001).
   *A. P. Young, //Notes on the replica symmetric solution of the classical and quantum SK model, including the matrix of second derivatives and the spin glass susceptibility//, [[https://doi.org/10.48550/arXiv.1706.07315|arXiv:1706.07315]].   *A. P. Young, //Notes on the replica symmetric solution of the classical and quantum SK model, including the matrix of second derivatives and the spin glass susceptibility//, [[https://doi.org/10.48550/arXiv.1706.07315|arXiv:1706.07315]].
  
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