Critical exponents of random XX and XY chains: Exact results via random walks

We study random XY and (dimerized) XX spin-1/2 quantum spin chains at their quantum phase transition driven by the anisotropy and dimerization, respectively. Using exact expressions for magnetization, correlation functions and energy gap, obtained by the free fermion technique, the critical and off-critical (Griffiths-McCoy) singularities are related to persistence properties of random walks. In this way we determine exactly the decay exponents for surface and bulk transverse and longitudinal correlations, correlation length exponent and dynamical exponent.Comment: 4 pages RevTeX, 1 eps-figure include

Nonequilibrium Dynamics and Aging in the Three--Dimensional Ising Spin Glass Model

The low temperature dynamics of the three dimensional Ising spin glass in zero field with a discrete bond distribution is investigated via MC simulations. The thermoremanent magnetization is found to decay algebraically and the temperature dependent exponents agree very well with the experimentally determined values. The nonequilibrium autocorrelation function $C(t,t_w)$ shows a crossover at the waiting (or {\em aging}) time $t_w$ from algebraic {\em quasi-equilibrium} decay for times $t$$\ll$$t_w$ to another, faster algebraic decay for $t$$\gg$$t_w$ with an exponent similar to one for the remanent magnetization.Comment: Revtex, 11 pages + 4 figures (included as Latex-files

Domain Growth in Random Magnets

We study the kinetics of domain growth in ferromagnets with random exchange interactions. We present detailed Monte Carlo results for the nonconserved random-bond Ising model, which are consistent with power-law growth with a variable exponent. These results are interpreted in the context of disorder barriers with a logarithmic dependence on the domain size. Further, we clarify the implications of logarithmic barriers for both nonconserved and conserved domain growth.Comment: 7 pages, 4 figure

Griffiths-McCoy singularities in the transverse field Ising model on the randomly diluted square lattice

The site-diluted transverse field Ising model in two dimensions is studied with Quantum-Monte-Carlo simulations. Its phase diagram is determined in the transverse field (Gamma) and temperature (T) plane for various (fixed) concentrations (p). The nature of the quantum Griffiths phase at zero temperature is investigated by calculating the distribution of the local zero-frequency susceptibility. It is pointed out that the nature of the Griffiths phase is different for small and large Gamma.Comment: 21 LaTeX (JPSJ macros included), 12 eps-figures include

Infinite disorder scaling of random quantum magnets in three and higher dimensions

Using a very efficient numerical algorithm of the strong disorder renormalization group method we have extended the investigations about the critical behavior of the random transverse-field Ising model in three and four dimensions, as well as for Erd\H os-R\'enyi random graphs, which represent infinite dimensional lattices. In all studied cases an infinite disorder quantum critical point is identified, which ensures that the applied method is asymptotically correct and the calculated critical exponents tend to the exact values for large scales. We have found that the critical exponents are independent of the form of (ferromagnetic) disorder and they vary smoothly with the dimensionality.Comment: 6 pages, 5 figure

Gamma ray emission and stochastic particle acceleration in galaxy clusters

FERMI (formely GLAST) will shortly provide crucial information on relativistic particles in galaxy clusters. We discuss non-thermal emission in the context of general calculations in which relativistic particles (protons and secondary electrons due to proton-proton collisions) interact with MHD turbulence generated in the cluster volume during cluster mergers. Diffuse cluster-scale radio emission (Radio Halos) and hard X-rays are produced during massive mergers while gamma ray emission, at some level, is expected to be common in galaxy clusters.Comment: 4 pages, 2 Figure, proc. of the 4th Heidelberg International Symposium on High Energy Gamma-ray Astronom

Finite Size Scaling Analysis of Exact Ground States for +/-J Spin Glass Models in Two Dimensions

With the help of EXACT ground states obtained by a polynomial algorithm we compute the domain wall energy at zero-temperature for the bond-random and the site-random Ising spin glass model in two dimensions. We find that in both models the stability of the ferromagnetic AND the spin glass order ceases to exist at a UNIQUE concentration p_c for the ferromagnetic bonds. In the vicinity of this critical point, the size and concentration dependency of the first AND second moment of the domain wall energy are, for both models, described by a COMMON finite size scaling form. Moreover, below this concentration the stiffness exponent turns out to be slightly negative \theta_S = -0.056(6) indicating the absence of any intermediate spin glass phase at non-zero temperature.Comment: 7 pages Latex, 5 postscript-figures include

Soil survey series 17

UNITED STATES DEPARTMENT OF AGRICULTURE Soil Conservation Service and UNITED STATES DEPARTMENT OF THE INTERIOR Bureau of Land Management In cooperation with ALASKA AGRICULTURAL EXPERIMENT STATIO

Extended surface disorder in the quantum Ising chain

We consider random extended surface perturbations in the transverse field Ising model decaying as a power of the distance from the surface towards a pure bulk system. The decay may be linked either to the evolution of the couplings or to their probabilities. Using scaling arguments, we develop a relevance-irrelevance criterion for such perturbations. We study the probability distribution of the surface magnetization, its average and typical critical behaviour for marginal and relevant perturbations. According to analytical results, the surface magnetization follows a log-normal distribution and both the average and typical critical behaviours are characterized by power-law singularities with continuously varying exponents in the marginal case and essential singularities in the relevant case. For enhanced average local couplings, the transition becomes first order with a nonvanishing critical surface magnetization. This occurs above a positive threshold value of the perturbation amplitude in the marginal case.Comment: 15 pages, 10 figures, Plain TeX. J. Phys. A (accepted