Percolation transition in a two-dimensional system of Ni granular ferromagnets

Abstract

We model magnetotransport features of the quenched condensed granular Ni thin films by a random two-dimensional resistor network in order to test the condition where a single bond dominates the system. The hopping conductivity is assumed to depend on the distance between neighboring ferromagnetic grains and the mutual orientation of the magnetic moments of these grains. We find that the quantity characterizing the transition from weak disorder (not sensitive to a change of a single bond resistivity) to strong disorder (very sensitive to such changes) scales as kappa/L(1/1.3), where L is the size of the system and kappa is a measure of disorder.

Universal Behavior of Optimal Paths in Weighted Networks with General Disorder

“…It is plausible that the criterion of Eq. (8) is valid also for other properties in weighted networks -such as conductivity and flow in random resistor networks -due to a recently-found close relation between the optimal path and flow [3,19].…”

“…We begin with the well-studied exponential disorder function f (x) = e ax , where x is a random number between 0 and 1 [2,3]. From Eq.…”

“…The study of the optimal path in disordered networks has attracted much interest in recent years, due to its relation to many complex systems of interest, including polymers [1,2], nanomagnet transport [3], surface growth [4], spin glasses [5], tumoral growth immune response [6], and complex networks [7]. The disorder is realized by assigning random weights w to the links of the network, where the weights are drawn from a distribution P (w), chosen to reflect the characteristics of the system under study.…”

“…The disorder is realized by assigning random weights w to the links of the network, where the weights are drawn from a distribution P (w), chosen to reflect the characteristics of the system under study. Examples include exponential disorder for tunnelling effects [3], power law disorder for driven diffusion in random media [8], lognormal distribution in conductance of quantum dots [9] and Gaussian distribution for polymers [10].…”

Current flow in random resistor networks: The role of percolation in weak and strong disorder

“…Examples include flow through porous material, oil production, and conductivity of semiconducting materials or metal-insulator mixtures [1,2,3,4,5,6,7,8,9,10]. These problems have been studied using a random resistor network model with bonds that have a resistance chosen from a probability distribution mimicking the nature of the physical problem under consideration.…”