Related papers: Finite-time scaling at the Anderson transition for…
We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the…
We conduct a numerical study of wave localization in disordered three-dimensional non-Hermitian systems featuring exceptional points. The energy spectrum of a disordered non-Hermitian Hamiltonian, exhibiting both parity-time and…
A mixture of two fermionic species with different masses is studied in an optical lattice. The heavy fermions are subject only to thermal fluctuations, the light fermions also to quantum fluctuations. We derive the Ising-like distribution…
A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of…
The solid--fluid phase transition of a granular material shaken horizontally is investigated numerically. We find that it is a second-order phase transition and propose two order parameters, namely the averaged kinetic energy and the…
We propose a scaling ansatz for the elastic energy of a system near the critical jamming transition in terms of three relevant fields: the compressive strain $\Delta \phi$ relative to the critical jammed state, the shear strain $\epsilon$,…
We examine the localization properties of the three-dimensional (3D) Anderson Hamiltonian with off-diagonal disorder using the transfer-matrix method (TMM) and finite-size scaling (FSS). The nearest-neighbor hopping elements are chosen…
Via a combination of molecular dynamics (MD) simulations and finite-size scaling (FSS) analysis, we study dynamic critical phenomena for the vapor-liquid transition in a three dimensional Lennard-Jones system. The phase behavior of the…
For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
The random-field Ising model shows extreme critical slowdown that has been described by activated dynamic scaling: the characteristic time for the relaxation to equilibrium diverges exponentially with the correlation length, $\ln \tau\sim…
Elasto-plastic models are among the most successful ways to study the critical properties of the plastic yielding transition of amorphous solids. Typically these models are studied under a condition of constant transition rates from one…
Using the level--spacing distribution and the total probability function of the numbers of levels in a given energy interval we analyze the crossover of the level statistics between the delocalized and the localized regimes. By numerically…
We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
Systems which can spontaneously reveal periodic evolution are dubbed time crystals. This is in analogy with space crystals that display periodic behavior in configuration space. While space crystals are modelled with the help of space…
The three-dimensional Anderson model represents a paradigmatic model to understand the Anderson localization transition. In this work we first review some key results obtained for this model in the past 50 years, and then study its…
We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. The focus is on the case of coordination number $m+1 = 3$, with a box distribution of…
We consider discrete models of kinetic rough interfaces that exhibit space-time scale-invariance in height-height correlation. A generic scaling theory implies that the dynamical structure factor of the height profile can uniquely…