Ferrimagnetism of dilute Ising antiferromagnets

It is shown that nearest-neighbor antiferromagnetic interactions of identical Ising spins on imbalanced bipartite lattice and imbalanced bipartite hierarchical fractal result in ferrimagnetic order instead of antiferromagnetic one. On some crystal lattices dilute Ising antiferromagnets may also become ferrimagnets due to the imbalanced nature of the magnetic percolation cluster when it coexists with the percolation cluster of vacancies. As evidenced by the existing experiments on $Fe_pZn_{1-p}F_2$, such ferrimagnetism is inherent property of bcc lattice so thermodynamics of these compounds at low $p$ can be similar to that of antiferromagnet on imbalanced hierarchical fractal.Comment: 6 pages, 4 figure

Equilibrium random-field Ising critical scattering in the antiferromagnet Fe(0.93)Zn(0.07)F2

It has long been believed that equilibrium random-field Ising model (RFIM) critical scattering studies are not feasible in dilute antiferromagnets close to and below Tc(H) because of severe non-equilibrium effects. The high magnetic concentration Ising antiferromagnet Fe(0.93)Zn(0.07)F2, however, does provide equilibrium behavior. We have employed scaling techniques to extract the universal equilibrium scattering line shape, critical exponents nu = 0.87 +- 0.07 and eta = 0.20 +- 0.05, and amplitude ratios of this RFIM system.Comment: 4 pages, 1 figure, minor revision

The Academics Athletics Trade-off: Universities and Intercollegiate Athletics

This analysis focuses on several key issues in the Football Bowl Subdivision (FBS). The intrinsic benefits of athletic programs are discussed in the first section. Trends in graduation rates and academic performance among athletes and how they correlate with the general student body are discussed in the second section. Finally, an overview of the revenues and expenses of athletic department budgets are discussed in an effort to gain a better understanding of the allocation of funds to athletics. In spite of recent growth in revenues and expenses, the athletic department budget comprises on average only 5 percent of the entire university budget at an FBS school, though spending and revenues have increased dramatically in recent years. In the grand scheme of things, American higher education faces several other, arguably more pressing, areas of reform. However, athletics is a significant and growing dimension of higher education that warrants in-depth examination

How a spin-glass remembers. Memory and rejuvenation from intermittency data: an analysis of temperature shifts

The memory and rejuvenation aspects of intermittent heat transport are explored theoretically and by numerical simulation for Ising spin glasses with short-ranged interactions. The theoretical part develops a picture of non-equilibrium glassy dynamics recently introduced by the authors. Invoking the concept of marginal stability, this theory links irreversible `intermittent' events, or `quakes' to thermal fluctuations of record magnitude. The pivotal idea is that the largest energy barrier $b(t_w,T)$ surmounted prior to $t_w$ by thermal fluctuations at temperature $T$ determines the rate $r_q \propto 1/t_w$ of the intermittent events occurring near $t_w$. The idea leads to a rate of intermittent events after a negative temperature shift given by $r_q \propto 1/t_w^{eff}$, where the `effective age' $t_w^{eff} \geq t_w$ has an algebraic dependence on $t_w$, whose exponent contains the temperatures before and after the shift. The analytical expression is verified by numerical simulations. Marginal stability suggests that a positive temperature shift $T \to T'$ could erase the memory of the barrier $b(t_w,T)$. The simulations show that the barrier $b(t_w,T') \geq b(t_w,T)$ controls the intermittent dynamics, whose rate is hence $r_q \propto 1/t_w$. Additional `rejuvenation' effects are also identified in the intermittency data for shifts of both signs.Comment: Revised introduction and discussion. Final version to appear in Journal of Statistical Mechanics: Theory and Experimen

Analysing and controlling the tax evasion dynamics via majority-vote model

Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on simple square lattices, Voronoi-Delaunay random lattices, Barabasi-Albert networks, and Erd\"os-R\'enyi random graphs. In the order to analyse and to control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhod of the noise critical $q_{c}$. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust and can be reproduced also through the nonequilibrium MVM on various topologies.Comment: 18 pages, 7 figures, LAWNP'09, 200

Analytical and computational study of magnetization switching in kinetic Ising systems with demagnetizing fields

An important aspect of real ferromagnetic particles is the demagnetizing field resulting from magnetostatic dipole-dipole interaction, which causes large particles to break up into domains. Sufficiently small particles, however, remain single-domain in equilibrium. This makes such small particles of particular interest as materials for high-density magnetic recording media. In this paper we use analytic arguments and Monte Carlo simulations to study the effect of the demagnetizing field on the dynamics of magnetization switching in two-dimensional, single-domain, kinetic Ising systems. For systems in the ``Stochastic Region,'' where magnetization switching is on average effected by the nucleation and growth of fewer than two well-defined critical droplets, the simulation results can be explained by the dynamics of a simple model in which the free energy is a function only of magnetization. In the ``Multi-Droplet Region,'' a generalization of Avrami's Law involving a magnetization-dependent effective magnetic field gives good agreement with our simulations.Comment: 29 pages, REVTeX 3.0, 10 figures, 2 more figures by request. Submitted Phys. Rev.

Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold

We consider the asymptotic behaviour of positive solutions $u(t,x)$ of the fast diffusion equation $u_t=\Delta (u^{m}/m)={\rm div} (u^{m-1}\nabla u)$ posed for x\in\RR^d, $t>0$, with a precise value for the exponent $m=(d-4)/(d-2)$. The space dimension is $d\ge 3$ so that $m<1$, and even $m=-1$ for $d=3$. This case had been left open in the general study \cite{BBDGV} since it requires quite different functional analytic methods, due in particular to the absence of a spectral gap for the operator generating the linearized evolution. The linearization of this flow is interpreted here as the heat flow of the Laplace-Beltrami operator of a suitable Riemannian Manifold (\RR^d,{\bf g}), with a metric ${\bf g}$ which is conformal to the standard \RR^d metric. Studying the pointwise heat kernel behaviour allows to prove {suitable Gagliardo-Nirenberg} inequalities associated to the generator. Such inequalities in turn allow to study the nonlinear evolution as well, and to determine its asymptotics, which is identical to the one satisfied by the linearization. In terms of the rescaled representation, which is a nonlinear Fokker--Planck equation, the convergence rate turns out to be polynomial in time. This result is in contrast with the known exponential decay of such representation for all other values of $m$.Comment: 37 page

Existence of radial stationary solutions for a system in combustion theory

In this paper, we construct radially symmetric solutions of a nonlinear noncooperative elliptic system derived from a model for flame balls with radiation losses. This model is based on a one step kinetic reaction and our system is obtained by approximating the standard Arrehnius law by an ignition nonlinearity, and by simplifying the term that models radiation. We prove the existence of 2 solutions using degree theory

Stochastic Hysteresis and Resonance in a Kinetic Ising System

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes at a temperature below $T_{c}$. For these restricted parameters, the magnetization switches through random nucleation of a single droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for the interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise.Comment: 35 pages. Submitted to Phys. Rev. E Minor revisions to the text and updated reference

Effects of boundary conditions on magnetization switching in kinetic Ising models of nanoscale ferromagnets

Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this article we consider the effects of boundary conditions on the switching phenomena. A rich range of behaviors is predicted by droplet theory: the specific mechanism by which switching occurs depends on the structure of the boundary, the particle size, the temperature, and the strength of the applied field. The theory predicts the existence of a peak in the switching field as a function of system size in both systems with periodic boundary conditions and in systems with boundaries. The size of the peak is strongly dependent on the boundary effects. It is generally reduced by open boundary conditions, and in some cases it disappears if the boundaries are too favorable towards nucleation. However, we also demonstrate conditions under which the peak remains discernible. This peak arises as a purely dynamic effect and is not related to the possible existence of multiple domains. We illustrate the predictions of droplet theory by Monte Carlo simulations of two-dimensional Ising systems with various system shapes and boundary conditions.Comment: RevTex, 48 pages, 13 figure