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Register a new userNature vs. Nurture: Predictability in Low-Temperature Ising Dynamics
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Consider a dynamical many-body system with a random initial state subsequently evolving through stochastic dynamics. What is the relative importance of the initial state (nature) vs. the realization of the stochastic dynamics (nurture) in predicting the final state? We examined this question for the two-dimensional Ising ferromagnet following an initial deep quench from $T=infty$ to $T=0$. We performed Monte Carlo studies on the overlap between identical twins raised in independent dynamical environments, up to size $L=500$. Our results suggest an overlap decaying with time as $t^{-theta_h}$ with $theta_h = 0.22 pm 0.02$; the same exponent holds for a quench to low but nonzero temperature. This heritability exponent may equal the persistence exponent for the 2D Ising ferromagnet, but the two differ more generally.
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We study low-temperature nucleation in kinetic Ising models by analytical and simulational methods, confirming the general result for the average metastable lifetime, <tau> = A*exp(beta*Gamma) (beta = 1/kT) [E. Jordao Neves and R.H. Schonmann, Commun. Math. Phys. 137, 209 (1991)]. Contrary to common belief, we find that both A and Gamma depend significantly on the stochastic dynamic. In particular, for a ``soft dynamic, in which the effects of the interactions and the applied field factorize in the transition rates, Gamma does NOT simply equal the energy barrier against nucleation, as it does for the standard Glauber dynamic, which does not have this factorization property.
Using Monte Carlo simulations, we study the character of the spin-glass (SG) state of a site-diluted dipolar Ising model. We consider systems of dipoles randomly placed on a fraction x of all L^3 sites of a simple cubic lattice that point up or down along a given crystalline axis. For x < 0.65 these systems are known to exhibit an equilibrium spin-glass phase below a temperature T_sg proportional to x. At high dilution and very low temperatures, well deep in the SG phase, we find spiky distributions of the overlap parameter q that are strongly sample-dependent. We focus on spikes associated with large excitations. From cumulative distributions of q and a pair correlation function averaged over several thousands of samples we find that, for the system sizes studied, the average width of spikes, and the fraction of samples with spikes higher than a certain threshold does not vary appreciably with L. This is compared with the behaviour found for the Sherrington-Kirkpatrick model.
Pyrochlore magnets are candidates for spin-ice behavior. We present theoretical simulations of relevance for the pyrochlore family R2Ti2O7 (R= rare earth) supported by magnetothermal measurements on selected systems. By considering long ranged dipole-dipole as well as short-ranged superexchange interactions we get three distinct behaviours: (i) an ordered doubly degenerate state, (ii) a highly disordered state with a broad transition to paramagnetism, (iii) a partially ordered state with a sharp transition to paramagnetism. Thus these competing interactions can induce behaviour very different from conventional ``spin ice. Closely corresponding behaviour is seen in the real compounds---in particular Ho2Ti2O7 corresponds to case (iii) which has not been discussed before, rather than (ii) as suggested earlier.
A metastable lattice gas with nearest-neighbor interactions and continuous-time dynamics is studied using a generalized Becker-Doring approach in the multidimensional space of cluster configurations. The pre-exponential of the metastable state lifetime (inverse of nucleation rate) is found to exhibit distinct peaks at integer values of the inverse supersaturation. Peaks are unobservable (infinitely narrow) in the strict limit T->0, but become detectable and eventually dominate at higher temperatures.
We present the stellar population properties of 13 dwarf galaxies residing in poor groups (low-density environment, LDE) observed with VIMOS@VLT. Ages, metallicities, and [alpha/Fe] ratios were derived from the Lick indices Hbeta, Mgb, Fe5270 and Fe5335 through comparison with our simple stellar population (SSP) models accounting for variable [alpha/Fe] ratios. For a fiducial subsample of 10 early-type dwarfs we derive median values and scatters around the medians of 5.7 pm 4.4 Gyr, -0.26 pm 0.28, and -0.04 pm 0.33 for age, log Z/Zsun, and [alpha/Fe], respectively. For a selection of bright early-type galaxies (ETGs) from the Annibali et al.2007 sample residing in comparable environment we derive median values of 9.8 pm 4.1 Gyr, 0.06 pm 0.16, and 0.18 pm 0.13 for the same stellar population parameters. It follows that dwarfs are on average younger, less metal rich, and less enhanced in the alpha-elements than giants, in agreement with the extrapolation to the low mass regime of the scaling relations derived for giant ETGs. From the total (dwarf + giant) sample we derive that age propto sigma^{0.39 pm 0.22}, Z propto sigma^{0.80 pm 0.16}, and alpha/Fe propto sigma^{0.42 pm 0.22}. We also find correlations with morphology, in the sense that the metallicity and the [alpha/Fe] ratio increase with the Sersic index n or with the bulge-to-total light fraction B/T. The presence of a strong morphology-[alpha/Fe] relation appears to be in contradiction to the possible evolution along the Hubble sequence from low B/T (low n) to high B/T (high n) galaxies. We also investigate the role played by environment comparing the properties of our LDE dwarfs with those of Coma red passive dwarfs from the literature. We find possible evidence that LDE dwarfs experienced more prolonged star formations than Coma dwarfs, however larger data samples are needed to draw more firm conclusions.
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