CONVEX REPLICA SYMMETRY BREAKING FROM POSITIVITY AND THERMODYNAMIC LIMIT
2004 ◽
Vol 18
(04n05)
◽
pp. 585-591
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Keyword(s):
Consider a correlated Gaussian random energy model built by successively adding one particle (spin) into the system and imposing the positivity of the associated covariance matrix. We show that the validity of a recently isolated condition ensuring the existence of the thermodynamic limit forces the covariance matrix to exhibit the Parisi replica symmetry breaking scheme with a convexity conditions on the matrix elements.
2015 ◽
Vol 49
(4)
◽
pp. 045002
Replica symmetry breaking, complexity and spin representation in the generalized random energy model
2010 ◽
Vol 43
(48)
◽
pp. 485004
◽
Keyword(s):
Keyword(s):
1995 ◽
Vol 28
(11)
◽
pp. 3093-3107
◽
Keyword(s):
Keyword(s):