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Volumn 81, Issue 18, 2010, Pages

Quantum mechanical and information theoretic view on classical glass transitions

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EID: 77955460497     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.184303     Document Type: Article
Times cited : (102)

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    • It is interesting to notice an important difference between this constructive scheme of a gaugeable glass and other disordered glassy systems. So long as the degeneracy can be understood in terms of essentially decoupled subsystems undergoing an ordering transition, it is bound to scale at most as exp ( Lθ ), with θ
    • It is interesting to notice an important difference between this constructive scheme of a gaugeable glass and other disordered glassy systems. So long as the degeneracy can be understood in terms of essentially decoupled subsystems undergoing an ordering transition, it is bound to scale at most as exp (L θ), with θ < d - 1, where d is the dimensionality of the system (if the interactions are short ranged). Indeed, an extensive degeneracy ∼ exp (L d) would require the existence of an ordering transition in subsystems composed of a finite number of degrees of freedom, which is not possible. The significance of this difference is underlined by the fact that several phenomenological approaches to understand dynamical glass transitions [for instance in terms of configurational entropy (Ref.)] rely on the extensivity of the glass degeneracy.
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    • We note in passing that if one promotes the J z x i / J = ± 1 and J y z i / J = ± 1 to dynamical variables as opposed to quenched random variables, with the contraint J z x i J y z i + x J z x i + y J y z i = J 4 yet enforced, the discussion above remains largely unchanged. However, in this case one has notably an example of a thermodynamic phase transition into a massively degenerate liquidlike phase (i.e., with no local order) in a nondisordered system.
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    • It is worth pointing out that, in this correspondence, a d -dimensional classical system endowed with a given Markov dynamics (i.e., with a specific "time dimension") maps onto a d -dimensional quantum system, encoding all the information from d spatial dimensions plus 1 (time)
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