Search results for "Universality"
showing 10 items of 107 documents
Kinetics of the Formation of Ordered Domains on Surfaces: Theoretical Considerations and Monte-Carlo Simulation
1986
When an adsorbed monolayer which initially is in a disordered state is suddenly brought to a temperature in the regime of the ordered phase, domains of the ordered phase are predicted to form and grow with time t after the quench according to a power law, i.e. linear dimension L(t) ∞ tx. At the same time, the structure function S(k,t) is predicted to satisfy a scaling law, S(k,t) = S(k,tx), k being the difference between the wave vector observed in the scattering and the Bragg wave vector describing the long range order. The theoretical ideas which lead to this behaviour are briefly reviewed, and evidence from simulations of simple lattice gas models and Potts models is presented. Particula…
Protein crystallization: universal thermodynamic vs. specific effects of PEG
2008
The interest of nucleation of protein crystals and aggregates (including oligomerization) spans from basic physics theory all the way to biophysics, nanophysics, clinical sciences, biotechnologies, food technologies and polymer–solvent interactions. Understanding nucleation within a theoretical framework capable of providing quantitative predictions and control of nucleation rates, or even the very occurrence of crystallization, is a long-sought goal of remarkable relevance to each of the above fields. A large amount of work has been aimed at such goal, but success has been so far rather limited. Work at our laboratory has more recently highlighted a direct link between nucleation rates and…
Chapter III Phase transitions at surfaces
1995
Abstract The statistical mechanics of phase transitions is briefly reviewed, with an emphasis on surfaces. Flat surfaces of crystals may act as a substrate for adsorption of two-dimensional (d=2) monolayers and multilayers, offering thus the possibility to study phase transitions in restricted dimensionality. Critical phenomena for special universality classes can thus be investigated which have no counterpart in d=3. Also phase transitions can occur that are in a sense “in between” different dimensionalities (e.g., multilayer adsorption and wetting phenomena are transitions in between two and three dimensions, while adsorption of monolayers on stepped surfaces allows phenomena in between o…
Konishi form factor at three loops in N=4 supersymmetric Yang-Mills theory
2017
We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction ($\overline{DR}$) scheme. We show that it satisfies the KG equation in $\overline{DR}$ scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality o…
Universal mechanism of spin relaxation in solids
2005
We consider relaxation of a rigid spin cluster in an elastic medium in the presence of the magnetic field. Universal simple expression for spin-phonon matrix elements due to local rotations of the lattice is derived. The equivalence of the lattice frame and the laboratory frame approaches is established. For spin Hamiltonians with strong uniaxial anisotropy the field dependence of the transition rates due to rotations is analytically calculated and its universality is demonstrated. The role of time reversal symmetry in spin-phonon transitions has been elucidated. The theory provides lower bound on the decoherence of any spin-based solid-state qubit.
Universality of Many-Body States in Rotating Bose and Fermi Systems
2008
We propose a universal transformation from a many-boson state to a corresponding many-fermion state in the lowest Landau level approximation of rotating many-body systems, inspired by the Laughlin wave function and by the Jain composite-fermion construction. We employ the exact-diagonalization technique for finding the many-body states. The overlap between the transformed boson ground state and the true fermion ground state is calculated in order to measure the quality of the transformation. For very small and high angular momenta, the overlap is typically above 90%. For intermediate angular momenta, mixing between states complicates the picture and leads to small ground-state overlaps at s…
Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture II: Intermediate Scattering Function and Dynamic Susceptibility
1995
We have performed a molecular dynamics computer simulation of a supercooled binary Lennard-Jones system in order to compare the dynamical behavior of this system with the predictions of the idealized version of mode-coupling theory (MCT). By scaling the time $t$ by the temperature dependent $\alpha$-relaxation time $\tau(T)$, we find that in the $\alpha$-relaxation regime $F(q,t)$ and $F_s(q,t)$, the coherent and incoherent intermediate scattering functions, for different temperatures each follows a $q$-dependent master curve as a function of scaled time. We show that during the early part of the $\alpha$-relaxation, which is equivalent to the late part of the $\beta$-relaxation, these mast…
Nonmonotonical crossover of the effective susceptibility exponent
1997
We have numerically determined the behavior of the magnetic susceptibility upon approach of the critical point in two-dimensional spin systems with an interaction range that was varied over nearly two orders of magnitude. The full crossover from classical to Ising-like critical behavior, spanning several decades in the reduced temperature, could be observed. Our results convincingly show that the effective susceptibility exponent gamma_eff changes nonmonotonically from its classical to its Ising value when approaching the critical point in the ordered phase. In the disordered phase the behavior is monotonic. Furthermore the hypothesis that the crossover function is universal is supported.
Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations
2012
One dimensional versions of cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. They can resolve a large range of time and length scales, and admit exact numerical integration. We use such models to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the 3D EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent \gamma depends on the initial conditions, characterized by th…
Critical Attractor and Universality in a Renormalization Scheme for Three Frequency Hamiltonian Systems
1998
We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for three degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.