Temperature Chaos, Rejuvenation and Memory in Migdal-Kadanoff Spin Glasses

We use simulations within the Migdal-Kadanoff real space renormalization approach to probe the scales relevant for rejuvenation and memory in spin glasses. One of the central questions concerns the role of temperature chaos. First we investigate scaling laws of equilibrium temperature chaos, finding super-exponential decay of correlations but no chaos for the total free energy. Then we perform out of equilibrium simulations that follow experimental protocols. We find that: (1) rejuvenation arises at a length scale smaller than the ``overlap length'' l(T,T'); (2) memory survives even if equilibration goes out to length scales much larger than l(T,T').Comment: 4 pages, 4 figures, added references, slightly changed content, modified Fig.

A generalized Macdonald operator

We present an explicit difference operator diagonalized by the Macdonald polynomials associated with an (arbitrary) admissible pair of irreducible reduced crystallographic root systems. By the duality symmetry, this gives rise to an explicit Pieri formula for the Macdonald polynomials in question. The simplest examples of our construction recover Macdonald's celebrated difference operators and associated Pieri formulas pertaining to the minuscule and quasi-minuscule weights. As further by-products, explicit expansions and Littlewood-Richardson type formulas are obtained for the Macdonald polynomials associated with a special class of small weights.Comment: 11 pages. To appear in Int. Math. Res. Not. IMR

Field-Shift Aging Protocol on the 3D Ising Spin-Glass Model: Dynamical Crossover between the Spin-Glass and Paramagnetic States

Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model under a static magnetic field $h$ are examined by means of the standard Monte Carlo simulation on the field-shift aging protocol at temperature $T$. For each process with (T; \tw, h), \tw being the waiting time before the field is switched on, we extract the dynamical crossover time, \tcr(T; \tw, h). We have found a nice scaling relation between the two characteristic length scales which are properly determined from \tcr and \tw and then are normalized by the static field crossover length introduced in the SG droplet theory. This scaling behavior implies the instability of the SG phase in the equilibrium limit even under an infinitesimal $h$. In comparison with this numerical result the field effect on real spin glasses is also discussed.Comment: 4 pages, 5 figures, jpsj2, Changed conten

Real space application of the mean-field description of spin glass dynamics

The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard `mean-field theory' versus `droplet picture' debate of the last decades. The main predictions of both theories concerning the spin glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of the spin glass coherence length which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed.Comment: 4 pages, 4 eps figures. v2: published versio

Giant Rashba splitting of quasi-1D surface states on Bi/InAs(110)-(2×\times1)

Electronic states on the Bi/InAs(110)-(2$\times$1) surface and its spin-polarized structure are revealed by angle-resolved photoelectron spectroscopy (ARPES), spin-resolved ARPES, and density-functional-theory calculation. The surface state showed quasi-one-dimensional (Q1D) dispersion and a nearly metallic character; the top of the hole-like surface band is just below the Fermi level. The size of the Rashba parameter ($\alpha_{\rm R}$) reached quite a large value ($\sim$5.5 eV\AA). The present result would provide a fertile playground for further studies of the exotic electronic phenomena in 1D or Q1D systems with the spin-split electronic states as well as for advanced spintronic devices.Comment: 8 pages (double column), 7 figures and 1 tabl

Aging, rejuvenation and memory effects in Ising and Heisenberg spin glasses

We have compared aging phenomena in the Fe_{0.5}Mn_{0.5}TiO_3 Ising spin glass and in the CdCr_{1.7}In_{0.3}S_4 Heisenberg-like spin glass by means of low-frequency ac susceptibility measurements. At constant temperature, aging obeys the same `$\omega t$ scaling' in both samples as in other systems. Investigating the effect of temperature variations, we find that the Ising sample exhibits rejuvenation and memory effects which are qualitatively similar to those found in other spin glasses, indicating that the existence of these phenomena does not depend on the dimensionality of the spins. However, systematic temperature cycling experiments on both samples show important quantitative differences. In the Ising sample, the contribution of aging at low temperature to aging at a slightly higher temperature is much larger than expected from thermal slowing down. This is at variance with the behaviour observed until now in other spin glasses, which show the opposite trend of a free-energy barrier growth as the temperature is decreased. We discuss these results in terms of a strongly renormalized microscopic attempt time for thermal activation, and estimate the corresponding values of the barrier exponent $\psi$ introduced in the scaling theories.Comment: 8 pages, including 6 figure