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--- 물리:무작위_에너지_모형 [2026/01/12 14:11] – [응축 현상] admin
+++ 물리:무작위_에너지_모형 [2026/01/12 15:37] (current) – [참여비율(participation ratio)] admin
@@ Line 45: / Line 45: @@
 $$
 양수 $X$에 대한 항등식 $X^{-2} = \int_0^\infty t \exp(-tX) dt$를 사용하여 $Y_N(\beta)$의 샘플 평균을 표현해보자.
-$$\mathbb{E}$$
+\begin{eqnarray*}
+\mathbb{E} \left[ Y_N(\beta) \right] &=& \left[ \sum_{j=1}^M \exp\left(-2\beta E_j \right)\right] \int_0^\infty t \exp\left[ -t \sum_{i=1}^M e^{-\beta E_i} \right]\\
+&=& \int_0^\infty t \left[ \sum_{j=1}^M \exp\left(-2\beta E_j \right)\right] \exp\left[ -t \sum_{i=1}^M e^{-\beta E_i} \right]\\
+&=& \int_0^\infty t \left[ \sum_{j=1}^M \exp\left(-2\beta E_j \right)\right] \exp\left[-te^{-\beta E_i}\right] \exp\left[ -t \sum_{i=1}^{M-1} e^{-\beta E_i} \right]\\
+\end{eqnarray*}
 =====$p$-스핀 상호작용 모형과의 관계=====