Critical dynamics of the dirty boson problem: Revisiting the equality z=d

Physical Review Letters

Volumn 98, Issue 24, 2007, Pages

  Weichman, Peter B ^a   Mukhopadhyay, Ranjan ^b  

^a BAE SYSTEMS   (United States)

^b CLARK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FREE ENERGY; MOLECULAR DYNAMICS; PHASE TRANSITIONS; SUPERFLUID HELIUM;

BOSE GLASS; CRITICALITY; SUPERFLUID TRANSITION;

BOSONS;

EID: 34547308803     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.98.245701     Document Type: Article

References (23)

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17. P.B. Weichman and R. Mukhopadhyay (unpublished).
18. M.E. Fisher, M.N. Barber, and D. Jasnow, Phys. Rev. A 8, 1111 (1973). Amazingly, the last section of this paper, containing a discussion of how finite-size scaling might lead to violations of the Josephson relation, proposes a mechanism very similar to ours: anomalously strong boundary condition dependence of tθ, the distance from the critical point, on the twist wave vector, k0. If tθ-t∼k02, they find υ=1-α. Here we find an even more anomalous linear dependence of δθ-δ on ω0, leading to υτ=-α. We are unaware of any classical model where the original proposed violation occurs. PLRAAN 1050-2947 10.1103/PhysRevA.8.1111
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21. There are dynamical scaling breakdown issues at the finite T lambda transition (described by the classical Model F equations) as well, where the finite κ argument now yields z=d/2. However, violations are possible where there exist two different dynamical exponents z1, z2 satisfying z1+z2=d. Only the mean (z1+z2)/2=d/2 enters the corresponding hydrodynamic correlation function [V. Dohm, Phys. Rev. B PRBMDO 0163-1829 44, 2697 (1991)]. 10.1103/PhysRevB.44.2697
22. In a perhaps related effect, the rigorous finite-size correlation length exponent inequality νFS 2/d for classical random systems [J.T. Chayes, L. Chayes, D.S. Fisher, and T. Spencer, Phys. Rev. Lett. PRLTAO 0031-9007 57, 2999 (1986)] 10.1103/PhysRevLett.57.2999
23. does not preclude a second "intrinsic" exponent ν with ν<2/d [F. Pázmándi, R. Scalettar, and G.T. Zimányi, Phys. Rev. Lett. PRLTAO 0031-9007 79, 5130 (1997)] 10.1103/PhysRevLett.79.5130