Search results for "Scaling"
showing 10 items of 754 documents
Effect of magnons on the temperature dependence and anisotropy of spin-orbit torque
2020
We investigate the influence of magnons on the temperature-dependence and the anisotropy of the spin-orbit torque (SOT). For this purpose we use 3rd order perturbation theory in the framework of the Keldysh formalism in order to derive suitable equations to compute the magnonic SOT. We find several contributions to the magnonic SOT, which depend differently on the spin-wave stiffness $\mathcal{A}$ and on the temperature $T$, with the dominating contribution scaling like $T^{2}/\mathcal{A}^{2}$. Based on this formalism we compute the magnonic SOT in the ferromagnetic Rashba model. For large Rashba parameters the magnonic SOT is strongly anisotropic and for small quasiparticle broadening it m…
Surface-induced disorder in body-centered-cubic alloys
2000
We present Monte Carlo simulations of surface induced disordering in a model of a binary alloy on a bcc lattice which undergoes a first order bulk transition from the ordered DO3 phase to the disordered A2 phase. The data are analyzed in terms of an effective interface Hamiltonian for a system with several order parameters in the framework of the linear renormalization approach due to Brezin, Halperin and Leibler. We show that the model provides a good description of the system in the vicinity of the interface. In particular, we recover the logarithmic divergence of the thickness of the disordered layer as the bulk transition is approached, we calculate the critical behavior of the maxima o…
Self-similarity and scaling of thermal shock fractures
2013
The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously growing and interacting cracks are used to obtain scaling relations for crack length and spacing. The numerical results predict that such process of pattern formation with quasi-static crack growth is not stable and at some point the excess energy leads to unstable propagation of one of the longest crack. The onset of instability has also been determined from numerical results.
Effective description of domain wall strings
2017
The analysis of domain wall dynamics is often simplified to one-dimensional physics. For domain walls in thin films, more realistic approaches require the description as two-dimensional objects. This includes the study of vortices and curvatures along the domain walls as well as the influence of boundary effects. Here we provide a theory in terms of soft modes that allows us to analytically study the physics of extended domain walls and their stability. By considering irregularly shaped skyrmions as closed domain walls, we analyze their plasticity and compare their dynamics with those of circular skyrmions. Our theory directly provides an analytical description of the excitation modes of ma…
Light scattering in inhomogeneous Tomonaga-Luttinger liquids
2012
We derive the dynamical structure factor for an inhomogeneous Tomonaga-Luttinger liquid as can be formed in a confined strongly interacting one-dimensional gas. In view of current experimental progress in the field, we provide a simple analytic expression for the light-scattering cross section, requiring only the knowledge of the density dependence of the ground-state energy, as they can be extracted e.g. from exact or Quantum Monte Carlo techniques, and a Thomas-Fermi description. We apply the result to the case of one-dimensional quantum bosonic gases with dipolar interaction in a harmonic trap, using an energy functional deduced from Quantum Monte Carlo computations. We find an universal…
Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases
2003
We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.
Mott transitions in the half-filled SU(2M) symmetric Hubbard model
2012
The Hubbard model with large orbital degeneracy has recently gained relevance in the context of ultracold earth alkali like atoms. We compute its static properties in the SU(2M) symmetric limit for up to M=8 bands at half filling within dynamical mean-field theory, using the numerically exact multigrid Hirsch-Fye quantum Monte Carlo approach. Based on this unbiased data, we establish scaling laws which predict the phase boundaries of the paramagnetic Mott metal-insulator transition at arbitrary orbital degeneracy M with high accuracy.
Critical behaviour of coupled spin chains
1991
The authors investigate, using numerical computation of the eigenvalues of short chains, the critical behaviour of two composite spin models, which interpolate smoothly between isotropic Heisenberg chains with different values of S. For the first model which interpolates between S=1/2 and S=3/2 they find that the model is critical over the whole range and the values of the central charge and critical exponents (scaling dimensions) appear to be constant in the thermodynamic limit. In the second model, which interpolates between S=1/2 and S=1 they find that, except at S=1/2, the central charge is effectively zero, implying a non-critical behaviour.
Finite-size scaling analysis of the anisotropic critical behavior of the two-dimensional Ising model under shear
2010
The critical behavior of the two-dimensional Ising Model with non-conserved order parameter in steady-state shear is studied by large-scale Monte Carlo simulations. Studying the structure factor S(qx,qy) in the disordered phase, the ratio of correlation length exponents νx/νy in the two lattice directions (x,y) is estimated, and the critical temperature is determined as a function of the shear rate as Tc() − Tc(0) ∝ with ≈0.45. Critical exponents β≈0.37, γ≈1.1, ; ν⊥≈0.46, ν∥≈1.38 are roughly compatible with anisotropic hyperscaling.
High-temperature series expansion for the relaxation times of the two dimensional Ising model
1995
We derive the high temperature series expansions for the two relaxation times of the single spin-flip kinetic Ising model on the square lattice. The series for the linear relaxation time τl is obtained with 20 non-trivial terms, and the analysis yields 2.183±0.005 as the value of the critical exponentΔl, which is equal to the dynamical critical exponentz in the two-dimensional case. For the non-linear relaxation time we obtain 15 non-trivial terms, and the analysis leads to the resultsΔnl = 2.08 ± 0.07. The scaling relationΔl −Δnl = β (β being the exponent of the order parameter) seems to be fulfilled, though the error bars ofΔnl are still quite substantial. In addition, we obtain the serie…