Universality class of replica symmetry breaking, scaling behavior, and the low-temperature fixed-point order function of the Sherrington-Kirkpatrick model (original) (raw)
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2005
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 non-trivial T->0-limit of the Parisi order function q(x) for the SK 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\leq a\leq infty where x/T->a at T=0 and \xi\approx 1.13\pm 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.
2021
We study in detail the dynamic scaling of the three-dimensional (3D) Ising model driven through its critical point on finite-sized lattices. We show explicitly that while finite-size scaling (FSS) at fixed driving rates and finite-time scaling (FTS) on fixed lattice sizes are satisfied for one set of all four observables we measure in their respective scaling regimes, they can be violated for the other set of the observables even in the same regimes. The different behaviors of the two sets of the observables indicate that the usual critical fluctuations can be divided into the so-called phases fluctuations and magnitude fluctuations. The self-similarity of criticality can also be divided into intrinsic and extrinsic self-similarities. The numerical results show that the phases fluctuations lead to the different behaviors while breaking the extrinsic self-similarity gives rise to the violations of the scalings. The set of the observables that violate the scalings is further divided i...
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