물리:드알메이다-사울레스_선

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물리:드알메이다-사울레스_선 [2026/09/28 14:02] – [강자성 해에서의 안정성] admin물리:드알메이다-사울레스_선 [2026/10/01 12:45] (current) – [감수율] admin
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-====감수율====+====비선형 감수율====
  
 다음과 같이 스핀 유리의 감수율을 정의하자: 다음과 같이 스핀 유리의 감수율을 정의하자:
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 \begin{eqnarray*} \begin{eqnarray*}
 \frac{1}{N} \sum_i \langle S_i^\alpha S_i^\beta \rangle &=& \lim_{n\to 0} \langle q_{\alpha\beta} \rangle\\ \frac{1}{N} \sum_i \langle S_i^\alpha S_i^\beta \rangle &=& \lim_{n\to 0} \langle q_{\alpha\beta} \rangle\\
-\frac{1}{N} \sum_i \langle S_i^\alpha S_i^\beta \langle S_i^\gamma S_i^\delta \rangle &=& \lim_{n\to 0} \left[ -(\beta J)^{-2} \delta_{\alpha\beta, \gamma\delta} + \langle q_{\alpha\beta} q_{\gamma\delta} \rangle \right].+\frac{1}{N} \sum_i \langle S_i^\alpha S_i^\beta \rangle \langle S_i^\gamma S_i^\delta \rangle &=& \lim_{n\to 0} \left[ -(\beta J)^{-2} \delta_{\alpha\beta, \gamma\delta} + \langle q_{\alpha\beta} q_{\gamma\delta} \rangle \right].
 \end{eqnarray*} \end{eqnarray*}
 그러므로 감수율은 이렇게 표현할 수 있다: 그러므로 감수율은 이렇게 표현할 수 있다:
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 \end{eqnarray*} \end{eqnarray*}
 로서 $\chi_\text{SG}^0 \equiv \beta^2(1-2q+r)$이다. 로서 $\chi_\text{SG}^0 \equiv \beta^2(1-2q+r)$이다.
 +
 +이 양이 발산하는 지점은 위에서 구한 드알메이다-사울레스 선과 일치한다.
 +
  
 ======함께 보기====== ======함께 보기======
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   *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]].
 +  *Tomoyuki Obuchi, //Role of the Finite Replica Analysis in the Mean-Field Theory of Spin Glasses//, [[https://arxiv.org/abs/1508.05225|arXiv:1508.05225]].
 +
  
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