Universality class for bootstrap percolation with m=3m=3 on the cubic lattice

We study the $m=3$ bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with probability $p$ or $1-p$, respectively. Occupied sites with less than $m$ occupied first-neighbours are then rendered unoccupied; this culling process is repeated until a stable configuration is reached. We evaluate the percolation critical probability, $p_c$, and both scaling powers, $y_p$ and $y_h$, and, contrarily to previous calculations, our results indicate that the model belongs to the same universality class as usual percolation (i.e., $m=0$). The critical spanning probability, $R(p_c)$, is also numerically studied, for systems with linear sizes ranging from L=32 up to L=480: the value we found, $R(p_c)=0.270 \pm 0.005$, is the same as for usual percolation with free boundary conditions.Comment: 11 pages; 4 figures; to appear in Int. J. Mod. Phys.

Frequency Modulation of Spin-Transfer Oscillators

Spin-polarized dc electric current flowing into a magnetic layer can induce precession of the magnetization at a frequency that depends on current. We show that addition of an ac current to this dc bias current results in a frequency modulated (FM) spectral output, generating sidebands spaced at the modulation frequency. The sideband amplitudes and shift of the center frequency with drive amplitude are in good agreement with a nonlinear FM model that takes into account the nonlinear frequency-current relation generally induced by spin transfer. Single-domain simulations show that ac current modulates the cone angle of the magnetization precession, in turn modulating the frequency via the demagnetizing field. These results are promising for communications and signal processing applications of spin-transfer oscillators.Comment: 13 pages, 3 Figure