Critical scaling in standard biased random walks

The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented with Monte Carlo simulations. We show that, for appropriate step sizes, the model displays a critical phenomenon, at $p=p_c$. Its scaling properties as well as the main features of the fragmented coverage occurring in the vicinity of the critical point are shown. In particular, in the limit $p\to p_c$, the distribution of fragment lengths is scale-free, with nontrivial exponents. Moreover, the spatial distribution of cracks (unvisited sites) defines a fractal set over the spanned interval. Thus, from the perspective of the covered territory, a very rich critical phenomenology is revealed in a simple one-dimensional standard model.Comment: 4 pages, 4 figure

Comparison of the electron-spin-resonance linewidth in multilayered CuMn spin glasses with insulating versus conducting interlayers

The temperature-dependent electron-spin-resonance linewidth ΔH(T) may be used to investigate the effect of the geometry and interlayer material on the magnetic properties of multilayered systems. We compare ΔH(T) in CuMn/Al2O3 multilayers with previous measurements of CuMn/Cu samples. CuMn/Al2O3 samples with CuMn thicknesses, WSG, from 40 Å to 20000 Å obey the same form as the CuMn/Cu system, but show quantitative differences in the fitting parameters. The linewidths of the CuMn/Al2O3 samples, even in the bulk, are systematically larger than the linewidths for the CuMn/Cu samples, suggesting that the ESR linewidth is sensitive to differences in sample growth and structure. The value of the minimum linewidth decreases with decreasing WSG in the CuMn/Al2O3 series, but remains constant in the CuMn/Cu series. Although susceptibility measurements of the freezing temperature Tf do not differentiate between samples with WSG≥5000 Å, the ESR linewidth is sensitive to changes at larger length scales. This experiment emphasizes the importance of considering both the total sample thickness, as defined by the range of the conduction electrons, and the spin-glass layer thickness in analyzing the ESR linewidth in multilayers