Percolation quantum phase transitions in diluted magnets

We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La2Cu(1-p)(Zn,Mg)(p)O4. Our results are also relevant for disordered interacting boson systems.     

Multicritical point in a diluted bilayer Heisenberg quantum antiferromagnet

The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed interlayer dimers is studied using quantum Monte Carlo simulations. A zero-temperature multicritical point (p(*),g(*)) at the classical percolation density p=p(*) and interlayer coupling g(*) approximately equal 0.16 is demonstrated. The quantum critical exponents of the percolating cluster are determined using finite-size scaling. It is argued that the associated finite-temperature quantum critical regime extends to zero interlayer coupling and could be relevant for antiferromagnetic cuprates doped with nonmagnetic impurities.     

Heisenberg-like ferromagnetism and percolative conductivity in the half-doped manganite Nd0.5Ca0.25Sr0.25MnO3

The magnetic behavior and electronic transport in the half-doped manganite Nd_0.5Ca_0.25Sr_0.25MnO₃ have been investigated. The critical exponents are studied by using isothermal magnetization methods. The results show that the paramagnetic-ferromagnetic transition is second order and the magnetic interaction is satisfied with the prediction of three-dimensional Heisenberg model. The electronic transport belongs to the percolation mechanism. These findings demonstrate that the critical behavior of the magnetic transition and conductivity for manganites are related to Mn-site ordering degree.     

Explosive percolation transition is actually continuous

Recently a discontinuous percolation transition was reported in a new "explosive percolation" problem for irreversible systems [D. Achlioptas, R. M. D'Souza, and J. Spencer, Science 323, 1453 (2009)] in striking contrast to ordinary percolation. We consider a representative model which shows that the explosive percolation transition is actually a continuous, second order phase transition though with a uniquely small critical exponent of the percolation cluster size. We describe the unusual scaling properties of this transition and find its critical exponents and dimensions.     

Quantum criticality and percolation in dimer-diluted two-dimensional antiferromagnets

The S = 1/2 Heisenberg model is considered on bilayer and single-layer square lattices with couplings J1, J2, with each spin belonging to one J2-coupled dimer. A transition from a Néel to disordered ground state occurs at a critical value of g = J2/J1. The systems are here studied at their dimer-dilution percolation points p*. The multicritical point (g*,p*) previously found for the bilayer is not reproduced for the single layer. Instead, there is a line of critical points (g < g*, p*) with continuously varying exponents. The uniform magnetic susceptibility diverges as T(-alpha) with alpha element of [1/2,1]. This unusual behavior is attributed to an effective free-moment density approximately T(1-alpha). The susceptibility of the bilayer is not divergent but exhibits remarkably robust quantum-critical scaling.     

Long-range connections, quantum magnets and dilute contact processes

In this article, we briefly review the critical behaviour of a long-range percolation model in which any two sites are connected with a probability that falls off algebraically with the distance. The results of this percolation transition are used to describe the quantum phase transitions in a dilute transverse Ising model at the percolation threshold p_c of the long-range connected lattice. In the similar spirit, we propose a new model of a contact process defined on the same long-range diluted lattice and explore the transitions at p_c. The long-range nature of the percolation transition allows us to evaluate some critical exponents exactly in both the above models. Moreover, mean field theory is valid for a wide region of parameter space. In either case, the strength of Griffiths McCoy singularities are tunable as the range parameter is varied.     

Ffast Transient Fluorescence Technique to Study Critical Exponents at the Glass Transition

The fast transient fluorescence (FTRF) technique was used to study critical exponents at the glass transition in free-radical crosslinking copolymerization (FCC) for two different monomeric systems, methyl methacrylate (MMA) and styrene (S). Pyrene (P_y ) was used as a fluorescence probe. The fluorescence lifetimes of P_y from its decay traces were measured and used to monitor the gelation process. Changes in the viscosity of the pregel solutions due to glass formation dramatically enhance the fluorescent yield of aromatic molecules. This effect is used to study the glass transition upon gelation of MMA and S monomeric systems as a function of time, at various temperatures and crosslinker concentrations. The results are interpreted in the view of percolation theory. The gel fraction and weight average degree of polymerization exponents β and γ are found to be 0.37 ± 0.02 and 1.66 ± 0.07 in agreement with percolation results.     

Magneto-transport of graphene and quantum phase transitions in the quantum Hall regime

In this paper we show the electronic transport and the quantum phase transitions that characterize the quantum Hall regime in graphene placed on SiO(2) substrates at magnetic fields up to 28 T and temperatures down to 4 K. The analysis of the temperature dependence of the Hall and longitudinal resistivity reveals intriguing non-universalities of the critical exponents of the plateau-insulator transition. These exponents depend on the type of disorder that governs the electrical transport and its characterization is important for the design and fabrication of novel graphene nano-devices.     

Conserved Manna model on Barabasi–Albert scale-free network

In this paper, a conserved Manna model is constructed and studied on Barabasi–Albert scale-free network with degree exponent γ = 3. Numerically I show that the system undergoes an absorbing state phase transition when the particle density is varied. Such a phase transition is characterized by measuring several critical exponents associated with the critical behaviour of the model. It has been found that the critical exponents exhibit mean field values of directed percolation. At the critical point, the spreading exponents have also been estimated. They satisfy the usual scaling relations. The effect of various initial conditions has been investigated and the result found to be independent of initial conditions, contrary to the fact that critical behaviour of such model highly depends on initial conditions when studied on regular lattice. The study confirms that though the Manna model in the lower dimensions exhibits different critical behavior other than DP, in the scale-free network it exhibits similar mean field result of DP class.     

Critical Behaviors and Universality Classes of Percolation Phase Transitions on Two-Dimensional Square Lattice

We have investigated both site and bond percolation on two-dimensional lattice under the random rule and the product rule respectively. With the random rule, sites or bonds are added randomly into the lattice. From two candidates picked randomly, the site or bond with the smaller size product of two connected clusters is added when the product rule is taken. Not only the size of the largest cluster but also its size jump are studied to characterize the universality class of percolation. The finite-size scaling forms of giant cluster size and size jump are proposed and used to determine the critical exponents of percolation from Monte Carlo data. It is found that the critical exponents of both size and size jump in random site percolation are equal to that in random bond percolation. With the random rule, site and bond percolation belong to the same universality class. We obtain the critical exponents of the site percolation under the product rule, which are different from that of both random percolation and the bond percolation under the product rule. The universality class of site percolation differs different from that of bond percolation when the product rule is used.     

Detecting topological order through a continuous quantum phase transition

We study a continuous quantum phase transition that breaks a Z2 symmetry. We show that the transition is described by a new critical point which does not belong to the Ising universality class, despite the presence of well-defined symmetry-breaking order parameter. The new critical point arises since the transition not only breaks the Z2 symmetry, it also changes the topological or quantum order in the two phases across the transition. We show that the new critical point can be identified in experiments by measuring critical exponents. So measuring critical exponents and identifying new critical points is a way to detect new topological phases and a way to measure topological or quantum orders in those phases.     

Criticality of Epidemic Spreading in Mobile Individuals Mediated by Environment

We investigate the critical behaviour of an epidemical model in a diffusive population mediated by a static vector environment on a 2D network. It is found that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behaviour near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.     

Dynamic transitions in Domany-Kinzel cellular automata on small-world network

We study Domany-Kinzel cellular automata on small-world network. Every link on a one dimensional chain is rewired and coupled with any node with probability p. We observe that, the introduction of long-range interactions does not remove the critical character of the model and the system still exhibits a well-defined phase transition to absorbing state. In case of directed percolation (DP), we observe a very anomalous behavior as a function of size. The system shows long lived metastable states and a jump in order parameter. This jump vanishes in thermodynamic limit and we recover second-order transition. The critical exponents are not equal to the mean-field values even for large p. However, for compact directed percolation(CDP), the critical exponents reach their mean-field values even for small p.     

Random-bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

We investigate the zero-temperature quantum phase transition of the randombond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter and correlation function probability distribution show a nontrivial scaling near the critical point, which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.     

一维自旋1键交替XXZ链中的量子纠缠和临界指数

利用基于张量网络表示的矩阵乘积态算法以及无限虚时间演化块抽取方法,本文研究了一维无限格点自旋1的键交替反铁磁XXZ海森伯模型中的量子相变.分别计算了系统的von Neumann熵、单位格点保真度和序参量,从而得到了系统随键交替强度的变化从拓扑有序Néel相到局域有序二聚化相的量子相变点.我们用矩阵乘积态方法拟合出了相变的中心荷c?0.5,表明此相变属于二维经典的Ising普适类.另外,通过对拓扑Néel序的数值拟合,我们得到了相变点处的特征临界指数β′=0.236和γ′=0.838.     

Random walk on topologically biased anisotropic percolation clusters and transport properties

Unbiased random walks are performed on topologically biased anisotropic percolation clusters (APC). Topologically biased APCs are generated using suitable anisotropic percolation models. New walk dimensions are found to characterize the anisotropic behaviour of the unbiased random walk on the biased topology. Critical properties of electro and magneto conductivities are characterized estimating respective dynamical critical exponents. A dynamical scaling theory relating dynamical and static critical exponents has been developed. The dynamical critical exponents satisfy the scaling relations within error bar.     

Measures of critical exponents in the four-dimensional site percolation

Using finite-size scaling methods we measure the thermal and magnetic exponents of the site percolation in four dimensions, obtaining a value for the anomalous dimension very different from the results found in the literature. We also obtain the leading corrections-to-scaling exponent and, with great accuracy, the critical density.     

Revisiting the nonequilibrium phase transition of the triplet-creation model

The nonequilibrium phase transition in the triplet-creation model is investigated using critical spreading and the conservative diffusive contact process. The results support the claim that at high enough diffusion the phase transition becomes discontinuous. As the diffusion probability increases the critical exponents change continuously from the ordinary directed percolation (DP) class to the compact directed percolation (CDP). The fractal dimension of the critical cluster, however, switches abruptly between those two universality classes. Strong crossover effects in both methods make it difficult, if not impossible, to establish the exact location of the tricritical point.     

Damage Spreading in a 2D Ising Model with Swendsen–Wang Dynamics

Damage spreading for Ising cluster dynamics is investigated numerically by using random numbers in a way that conforms with the notion of submitting the two evolving replicas to the same thermal noise. Two damage spreading transitions are found; damage does not spread either at low or high temperatures. We determine some critical exponents at the high-temperature transition point, which seem consistent with directed percolation.     

Universal behaviour of glass transition exponents in various polymeric systems

The fast transient fluorescence (FTRF) technique was used to study the critical exponents during glass transition in free-radical cross-linking copolymerization (FCC). Methyl methacrylate (MMA), ethyl methacrylate (EMA) and various combinations of MMA with EMA were used during FCC experiments. Pyrene (Py) was used as a fluorescence probe and its fluorescence lifetimes from its decay traces were measured during glass transition. Changes in the viscosity of the pre-gel solutions due to glass formation dramatically increased the Py fluorescent lifetimes, which were used to study the glass transition of MMA, EMA and their mixtures as a function of time, at various temperatures and monomer concentrations. The results were interpreted in the view of percolation theory. The critical exponents, β and γ, were measured near the glass transition point and found to be around 0.37 ± 0.015 and 1.69 ± 0.05, respectively, in all systems studied, which are in good agreement with the static percolation results.