We present a new family of percolation models. We show, using theory and computer simulations, that this class represents a new universality class. Interestingly, systems in this class appear to violate the Harris criterion, making model systems within this class ideal systems for studying the influence of disorder on critical behavior. We argue that such percolative systems have already been realized in practice in strongly correlated electron systems that have been driven to the quantum critical point by means of chemical substitution.

The presence of magnetic clusters has been verified in both antiferromagnetic and ferromagnetic quantum critical systems. We review some of the strongest evidence for strongly doped quantum critical systems (Ce(Ru0.24Fe0.76)2Ge2) and we discuss the implications for the response of the system when cluster formation is combined with finite size effects. In particular, we discuss the change of universality class that is observed close to the order-disorder transition. We detail the conditions under which clustering effects will play a significant role also in the response of stoichiometric systems and their experimental signature.

The onset of ordering in quantum critical systems is characterized by a competition between the Kondo shielding of magnetic moments and the ordering of these moments. We show how a distribution of Kondo shielding temperatures—resulting from chemical doping—leads to critical behavior whose main characteristics are given by percolation physics. With the aid of Monte Carlo computer simulations, we are able to infer the low temperature part of the distribution of shielding temperatures in heavily doped quantum critical Ce(Ru0.24Fe0.76)2Ge2. Based on this distribution, we show that the ordering dynamics—such as the growth of the correlation length upon cooling—can be understood by the spawning of magnetic clusters. Our findings explain why the search for universal exponents in quantum critical systems has been unsuccessful: the underlying percolation network associated with the chemical doping of quantum critical systems has to be incorporated in the modeling of these quantum critical systems.

The two B-site ions Mn 3+ and Mn 4+ in the stoichiometric spinel structure LiMn 2 O 4 form a complex, columnar ordered pattern below the charge-ordering transition at room temperature. On further cooling to below 66 K, the system develops long-range antiferromagnetic order. In contrast, whereas lithium-substituted Li͓Mn 2−x Li x ͔O 4 also undergoes a charge-ordering transition around room temperature, it only displays frozen in short-range magnetic order below ϳ25-30 K. We investigate to what extent the columnar charge-order pattern observed in LiMn 2 O 4 can account for the measured magnetic ordering patterns in both the pure and Li-substituted ͑x = 0.04͒ compounds. We conclude that eightfold rings of Mn 4+ ions form the main magnetic unit in both compounds ͑x = 0 , 0.04͒, and that clusters formed out of these rings act as superspins in the doped compound. The ground state properties of the known lithium-based cubic spinel compounds LiT 2 O 4 range from BCS superconductivity 1 ͓T =Ti͔, via heavy fermion behavior 2 ͓T =V͔ to frustrated antiferromagnetism 3,4 ͓T =Mn͔. In these systems, the divalent B-site ions ͑3+ and 4+͒ have an octahedral oxygen surrounding, while the Li + ions occupy the A-sites. In this paper we focus on the magnetism in the Mn compound. Above ϳ300 K, LiMn 2 O 4 is an electronhopping conductor, and the system undergoes a chargeordering ͑CO͒ transition on cooling down. Similar to the CO transition in magnetite, 5 the B-site octahedra are slightly deformed and a structural transition accompanies the CO transition. However, unlike for magnetite, the Mn 3+ -Mn 4+ charge-ordered structure has ͑most likely͒ been resolved by In stoichiometric LiMn 2 O 4 the Mn 3+ ions line up in columns along the c-axis 6 when cooled to below 300 K, see Fig. 1͑a͒. Multiple types of Mn 3+ sites can be distinguished. One type is located in cubes of four Mn 3+ ions and four O 2− ions ͑Mn-O distance= 2.05 Å͒ stacked along the c-direction. These cubes are at the center of eightfold rings of Mn 4+ ions. The Mn 4+ ions within these rings couple antiferromagnetically ͑AF͒ to each other through a 90°Mn-O-Mn exchange. The spaces in between neighboring rings are filled with the other types of Mn 3+ ions, which thus form columns in the c-direction. The unit cell ͑a = 24.74 Å, b = 24.84 Å, and c = 8.20 Å͒ houses eight eightfold rings. 6 The Mn 4+ rings only interact with other rings via the intervening Mn 3+ ions. When cooled to below 66 K, AF ordering develops, 7 but the ordered structure has not been resolved yet.The Li-doped material Li͓Mn 2−x Li x ͔O 4 has also been studied in detail 3,4 because of its applications as a battery material. 8 When a small amount of Li is substituted on the Mn sites, the material retains its capacity for removal of Li from the A-sites without affecting the overall spinel structure ͑hence its use in lithium batteries͒, but the ϳ300 K structural phase transition no longer takes place, even though the CO transition is unaffected. ͑Suppression of the structural transition greatly enhances the lif...

Order-disorder phase transitions in magnetic metals that occur at zero temperature have been studied in great detail. Theorists have advanced scenarios for these quantum critical systems in which the unusual response can be seen to evolve from a competition between ordering and disordering tendencies, driven by quantum fluctuations. Unfortunately, there is a potential disconnect between the real systems that are being studied experimentally, and the idealized systems that theoretical scenarios are based upon. Here we discuss how disorder introduces a change in morphology from a three-dimensional system to a collection of magnetic clusters, and we present neutron scattering data on a classical system, Li͓Mn Quantum fluctuations can be strong enough to prevent a system from ordering, even at 0 K. In metals that possess atomic magnetic moments, one can tweak the strength of the magnetic interactions compared to the disordering quantum fluctuations in such a way that the system orders exactly at 0 K. Such a system is said to be at the quantum critical point ͑QCP͒. The interest in such systems is easy to understand. One can expect a new type of ordering behavior because the spatial and temporal dimensions are no longer independent at 0 K.1 Also, one can expect new physics to emerge. After all, when a system is on the verge of ordering at 0 K, the degrees of freedom that prevent the system from ordering also provide a channel for the system to adopt a new, lower energy ground state. An example is the observed superconducting state 1 that forms close to the QCP with quasiparticles consisting of some admixture of magnetic moments and conduction electrons.The question that has attracted most attention is "what exactly happens at the QCP?" On the one hand, 2 it could be that all moments will become fully shielded at some finite temperature, with the residual interaction between the resulting heavy quasiparticles driving the system toward ordering ͓Fig. 1͑a͔͒. On the other hand, 2 the QCP could be the point in the phase diagram where vestiges of moments can survive all the way down to 0 K upon cooling without being completely screened though the Kondo effect, resulting in long-range order ͓Fig. 1͑b͔͒. Unfortunately, the experimental situation is much murkier than a simple choice between these two possible answers.To drive a system to a QCP, one tweaks the interaction between moments by changing the degree of overlap between the local atomic orbitals and the extended conduction electron bands. Ideally, one simply applies hydrostatic pressure to a system without any intrinsic disorder, and all magnetic moments will undergo the same temperature evolution. This is the situation that most theoretical efforts have focused on ͓Ref. 1͔. In some experiments however, one cannot attain the high pressures required and one results to applying chemical pressure. Here, some elements are substituted with different sized ones so as to achieve lattice expansion/ contraction at the cost of introducing some disorder. However, it was generally...