In this appendix we collect without derivation the for-mulas used in calculation of disorder properties. The derivation can be found in Mezard 共1991兲. The inverse matrix has the following Parisi parameters:
m =−1 1
m˜ −具m典
冉
1 −冕
01duu m˜ −具m典 − 关m兴关m兴u u− m0 m˜ −具m典
冊
;共B1兲 mx−1= − 1
m˜ −具m典
冉
x关m˜ − 具m典 − 关m兴关m兴x x兴 +冕
0xdv v2
关m兴v
m˜ −具m典 − 关m兴v
+ m0 m˜ −具m典
冊
.The square of the matrix can be treated similarly, m = 共m˜兲a,b2 2−具共mx兲2典,
共B2兲 共m2兲x= 2共m˜ − 具m典兲mx−
冕
0x
dv共mx− mv兲2.
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