Parisi’s Theory of Spin Glass

The spin-glass phase is characterized by the existence of many pure states due to random exchange interactions between spins. Parisi established the novel concept of replica symmetry breaking (RSB) from Sherrington Kirkpatrick’s mean-field theory via an abstract replica trick. In this article, his RSB scheme is reviewed from the view point of infinitely many pure states.

Entanglement between two gravitating universes

We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the n th Rényi entropy includes a wormhole between the n copies of the gravitating universe, leading to a standard “island formula” for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with 2n boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by Ζ n replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a “swap wormhole”, a geometry in which the boundaries of the two universes are glued together by a “swaperator”. This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes – a realization of the ER=EPR idea. The new wormhole restores unitarity of quantum information.

A transport equation approach for deep neural networks with quenched random weights

We consider a multi-layer Sherrington-Kirkpatrick spin-glass as a model for deep restricted Boltzmann machines with quenched random weights and solve for its free energy in the thermodynamic limit by means of Guerra's interpolating techniques under the RS and 1RSB ansatz. In particular, we recover the expression already known for the replica-symmetric case. Further, we drop the restriction constraint by introducing intra-layer connections among spins and we show that the resulting system can be mapped into a modular Hopfield network, which is also addressed via the same techniques up to the first step of replica symmetry breaking.

Orientation Kinetics of Chiral-Nematic N* Domains in Suspensions of Charged DNA Rods

Many biological systems exhibit natural regulation mechanisms as necessary functions. Proteins, peptides, charged receptors, RNAs, and DNAs clearly demonstrate such varieties of structural dynamics in their biocomplexity. To understand the proper structural functionality of biomolecules, this requires integrated information from initiation, regulation, transfer and transport to desirable sustainable processes. Here, we demonstrate the orientation kinetics of stable chiral-nematic (N*) domains that are consistently formed in the suspensions of charged DNA rods at low ionic strengths. This is enhanced by large access of released dissociated condensed ions and the mobile diffusive ions of DNA rods, acting onto the perpendicular motions of the DNA rods in bulk. The quantification of collective orientations for these interacting charged DNA rods is extracted by image-time correlation (ITC) performed in Fourier transforms (FTs) for overall spectral density distributions. Three distinguishable length scales are clearly shown corresponding to the relevant motion of the N* domain in parallel, perpendicular and the optical pitch within the domains as well as the kinetics of local distributions in FTs. Particularly strong concentration transitions are confirmed by replica symmetry breaking of elastic deformations in N* domains in terms of the average twist angle and the order parameter. This work can be interesting for sufficient cooling of the given concentration of charged DNA rods, at low ionic strengths (below the critical value), mimicking super-cooled liquid and orientation glass in other biomacromolecules.