Prof. David Sherrington FRS: Publications

Scaling and renormalization group in replica-symmetry-breaking space: evidence for a simple analytical solution of the Sherrington-Kirkpatrick model at zero temperature.

Phys Rev Lett 95:19 (2005) 197203

Authors:

R Oppermann, D Sherrington

Abstract:

Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB steps playing a role of decimation scales, we report evidence for a nontrivial T-->0 limit of the Parisi order function q(x) for the Sherrington-Kirkpatrick spin glass. Supported by scaling in RSB space, the fixed point order function is conjectured to be q*(a)=sqrt[pi]/2 a/xi erf(xi/a) on 0 a at T =0 and xi approximately 1.13+/-0.01. Xi plays the role of a correlation length in a-space. q*(a) may be viewed as the solution of an effective 1D field theory.

Exact mappings between fermionic Ising spin-glass and classical spin-glass models

Physical Review B: Condensed Matter and Materials Physics 72 (2005) 104427-1 to 104427-5

Authors:

D Sherrington, Isaac P\'erez Castillo

Strategy correlations and timing of adaptation in Minority Games

European Physical Journal B 45 (2005) 153 to 168

Authors:

D Sherrington, Tobias Galla

GLASSY BEHAVIOR DUE TO KINETIC CONSTRAINTS: FROM TOPOLOGICAL FOAM TO BACKGAMMON

Chapter in Current Topics in Physics, World Scientific Publishing (2005) 151-174

Glassy behavior in an exactly solved spin system with a ferromagnetic transition.

Phys Rev E Stat Nonlin Soft Matter Phys 71:3 Pt 2A (2005) 036112

Authors:

Robert L Jack, Juan P Garrahan, David Sherrington

Abstract:

We show that applying simple dynamical rules to Baxter's eight-vertex model leads to a system which resembles a glass-forming liquid. There are analogies with liquid, supercooled liquid, glassy, and crystalline states. The disordered phases exhibit strong dynamical heterogeneity at low temperatures, which may be described in terms of an emergent mobility field. Their dynamics are well described by a simple model with trivial thermodynamics, but an emergent kinetic constraint. We show that the (second order) thermodynamic transition to the ordered phase may be interpreted in terms of confinement of the excitations in the mobility field. We also describe the aging of disordered states toward the ordered phase, in terms of simple rate equations.

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