On the application of the Critical Minimum Energy Subspace method to disordered systems

Fragmentation and Novel Prethermal Dynamical Phases in Disordered, Strongly-Interacting Floquet Systems

We explore how disorder and interactions conspire in lattice models with sequentially activated hopping to produce novel k-body (or many-body) localized phases. Specifically, we show that when disorder is added to the set of interacting floquet models considered in [Wampler and Klich arXiv:2209.09180], regions in parameter space near the special points where classical-like dynamics emerge are stabilized prethermally (or via many-body localization in some cases) producing new families of interesting phases. We also find that this disordered system exhibits novel phases in regions of parameter s…

Locating the minimum : Approach to equilibrium in a disordered, symmetric zero range process

We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site $k$ hops to its nearest neighbour with a quenched rate $w(k)$. These rates are chosen randomly from the probability distribution $f(w) \sim (w-c)^{n}$, where $c$ is the lower cutoff. For $n > 0$, this model is known to exhibit a phase transition in the steady state from a low density phase with a finite number of particles at each site to a high density aggregate phase in which the site with the lowest hopping rate supports an infinite number of particles. In the …

Typical and large-deviation properties of minimum-energy paths on disordered hierarchical lattices

We perform numerical simulations to study the optimal path problem on disordered hierarchical graphs with effective dimension d=2.32. Therein, edge energies are drawn from a disorder distribution that allows for positive and negative energies. This induces a behavior which is fundamentally different from the case where all energies are positive, only. Upon changing the subtleties of the distribution, the scaling of the minimum energy path length exhibits a transition from self-affine to self-similar. We analyze the precise scaling of the path length and the associated ground-state energy fluct…

无序伊辛系统有效模型推断中的共识

Consensus in Effective Model Inference for Disordered Ising Systems

本文通过教师-学生框架研究无序伊辛系统，发现独立学习器推断的共识宽度在临界区最小，但错误设定偏差使最一致温度不同于最忠实温度。

From Brittle to Ductile Fracture in Disordered Materials

We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown to correspond to minimum energy surfaces. The similarity of the resulting fracture paths to the limits of brittle fracture or minimum energy surfaces is quantified. The model exhibits a smooth transition from brittleness to ductility. The dynamics of yielding exhibits avalanches with a power-law distribution.

Optimization and plasticity in disordered media

We study the plastic yielding of disordered media using the perfectly plastic random fuse model. The yield surfaces are shown to be different from those obtained minimizing the sum of the local yield thresholds, i.e. the so-called minimum 'energy' surfaces. As a result, the global yield stress is lower than expected from naive optimization and the difference persists as the sample size increases. At variance with minimum energy surfaces, height-height fluctuations of yield surfaces exhibit multiscaling. We provide a theoretical argument that explains how this behavior arises from the very diff…