Scaling, domains, and states in the four-dimensional random field Ising magnet

The four dimensional Gaussian random field Ising magnet is investigated numerically at zero temperature, using samples up to size $64^4$, to test scaling theories and to investigate the nature of domain walls and the thermodynamic limit. As the magnetization exponent $\beta$ is more easily distinguishable from zero in four dimensions than in three dimensions, these results provide a useful test of conventional scaling theories. Results are presented for the critical behavior of the heat capacity, magnetization, and stiffness. The fractal dimensions of the domain walls at criticality are estimated. A notable difference from three dimensions is the structure of the spin domains: frozen spins of both signs percolate at a disorder magnitude less than the value at the ferromagnetic to paramagnetic transition. Hence, in the vicinity of the transition, there are two percolating clusters of opposite spins that are fixed under any boundary conditions. This structure changes the interpretation of the domain walls for the four dimensional case. The scaling of the effect of boundary conditions on the interior spin configuration is found to be consistent with the domain wall dimension. There is no evidence of a glassy phase: there appears to be a single transition from two ferromagnetic states to a single paramagnetic state, as in three dimensions. The slowing down of the ground state algorithm is also used to study this model and the links between combinatorial optimization and critical behavior.Comment: 13 pages, 16 figure

Selenium and vascular health

Peer reviewedPublisher PD

Single and pair production of heavy leptons in E6E_6 model

We investigate the single and pair production of new heavy leptons via string inspired $E_{6}$ model at future linear colliders. Signal and corresponding backgrounds for these leptons are studied. We have found that single production of heavy leptons is more relevant than that of pair production, as expected. For a maximal mixing value of 0.1, the upper mass limits of 2750 GeV in the single case and 1250 GeV in the pair production case are obtained at $\sqrt{s}=3$ TeV collider option.Comment: 14 pages, 10 figure

GERT simulation program for GERT network analysis

GERT Simulation Program simulates GERT networks to obtain statistics on specified nodes of the network. It performs sampling experiments to determine which branches of the network are taken and how long it takes to traverse a branch of the network

Effects of Disorder on Electron Transport in Arrays of Quantum Dots

We investigate the zero-temperature transport of electrons in a model of quantum dot arrays with a disordered background potential. One effect of the disorder is that conduction through the array is possible only for voltages across the array that exceed a critical voltage $V_T$. We investigate the behavior of arrays in three voltage regimes: below, at and above the critical voltage. For voltages less than $V_T$, we find that the features of the invasion of charge onto the array depend on whether the dots have uniform or varying capacitances. We compute the first conduction path at voltages just above $V_T$ using a transfer-matrix style algorithm. It can be used to elucidate the important energy and length scales. We find that the geometrical structure of the first conducting path is essentially unaffected by the addition of capacitive or tunneling resistance disorder. We also investigate the effects of this added disorder to transport further above the threshold. We use finite size scaling analysis to explore the nonlinear current-voltage relationship near $V_T$. The scaling of the current $I$ near $V_T$, $I\sim(V-V_T)^{\beta}$, gives similar values for the effective exponent $\beta$ for all varieties of tunneling and capacitive disorder, when the current is computed for voltages within a few percent of threshold. We do note that the value of $\beta$ near the transition is not converged at this distance from threshold and difficulties in obtaining its value in the $V\searrow V_T$ limit