Heisenberg-like critical properties in ferromagnetic Nd1-xPbxMnO3 single crystals

Static magnetization for single crystals of insulating Nd0.85Pb0.15MnO3 and marginally conducting Nd0.70Pb0.30MnO3 has been studied around the ferromagnetic to paramagnetic transition temperature T-C. Results of measurements carried out in the critical range vertical bar(T - T-C)/T-C vertical bar <= 0.1 are reported. Critical exponents beta and gamma for the thermal behaviour of magnetization and susceptibility have been obtained both by modified Arrott plots and the Kouvel-Fisher method. The exponent delta independently obtained from the critical isotherm was found to satisfy the Widom scaling relation delta = gamma/beta + 1. For both compositions the values of exponents are consistent with those expected for isotropic magnets belonging to the Heisenberg universality class with short-range exchange in three dimensions. Correspondingly, the specific heat displays only a cusp-like anomaly at the critical temperature of these crystals which is consistent with an exponent alpha < 0. The results show that the ferromagnetic ordering transition in Nd1-xPbxMnO3 in the composition range 0.15 <= x <= 0.40 is continuous. This mixed-valent manganite displays the conventional properties of a Heisenberg-like ferromagnet, irrespective of the differing transport properties and in spite of low ordering temperatures T-C = 109 and 147.2 K for x = 0.15 and 0.30, respectively.

Quenching across quantum critical points: Role of topological patterns

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z(2) invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent nu being different in different sectors. Copyright (C) EPLA, 2010

Critical properties of the double-exchange ferromagnet Nd(0.6)Pb(0.4)MnO(3)

Results of a study of dc magnetization M(T,H), performed on a Nd(0.6)Pb(0.4)MnO(3) single crystal in the temperature range around T(C) (Curie temperature) which embraces the supposed critical region \epsilon\=\T-T(C)\/T(C)less than or equal to0.05 are reported. The magnetic data analyzed in the critical region using the Kouvel-Fisher method give the values for the T(C)=156.47+/-0.06 K and the critical exponents beta=0.374+/-0.006 (from the temperature dependence of magnetization) and gamma=1.329+/-0.003 (from the temperature dependence of initial susceptibility). The critical isotherm M(T(C),H) gives delta=4.54+/-0.10. Thus the scaling law gamma+beta=deltabeta is fulfilled. The critical exponents obey the single scaling equation of state M(H,epsilon)=epsilon(beta)f(+/-)(H/epsilon(beta+gamma)), where f(+) for T>T(C) and f(-) for Texponent values are very close to those expected for the universality class of three-dimensional Heisenberg ferromagnets with short-range interactions.

Critical behavior of brittle-ductile transition of polymers

We report that the brittle-ductile transition of polymers induced by temperature exhibits critical behavior. When t close to 0, the critical surface to surface interparticle distance (IDc) follows the scaling law: IDc proportional to t(-v) where t = 1 - T/T-BD(m) (T and T-BD(m) are the test temperature and brittle-ductile transition temperature of matrix polymer, respectively) and v = 2/D. It is clear that the scaling exponent v only depends on dimension (D). For 2, 3, and 4 dimension, v = 1, 2/3, and 1/2 respectively. The result indicates that the ID, follows the same scaling law as that of the correlation length (xi), when t approach to zero.

Gál-type GCD sums beyond the critical line

We prove that ∑k,ℓ=1N(nk,nℓ)2α(nknℓ)α≪N2−2α(logN)b(α) holds for arbitrary integers 1≤n1<⋯exponent b(α)b(α). This estimate complements recent results for 1/2≤α≤11/2≤α≤1 and shows that there is no “trace” of the functional equation for the Riemann zeta function in estimates for such GCD sums when 0<α<1/20<α<1/2.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Finding critical exponents for two-dimensional Hamiltonian maps

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The aggregation process in tetraethoxysilane-derived sonogels as an analogy to the critical phenomenon

The structural evolution in silica sols prepared from tetraethoxysilane (TEOS) sonohydrolysis was studied 'in situ' using small-angle x-ray scattering (SAXS). The structure of the gelling system can be reasonably well described by a correlation function given by gamma(r) similar to (1/R(2))(1/r) exp(- r/xi), where xi is the structure correlation length and R is a chain persistence length, as an analogy to the Ornstein-Zernike theory in describing critical phenomenon. This approach is also expected for the scattering from some linear and branched molecules as polydisperse coils of linear chains and random f-functional branched polycondensates. The characteristic length. grows following an approximate power law with time t as xi similar to t(1) (with the exponent quite close to 1) while R remains undetermined but with a constant value, except at the beginning of the process in which the growth of. is slower and R increases by only about 15% with respect to the value of the initial sol. The structural evolution with time is compatible with an aggregation process by a phase separation by coarsening. The mechanism of growth seems to be faster than those typically observed for pure diffusion controlled cluster-cluster aggregation. This suggests that physical forces (hydrothermal forces) could be actuating together with diffusion in the gelling process of this system. The data apparently do not support a spinodal decomposition mechanism, at least when starting from the initial stable acid sol studied here.

Quasilinear dirichlet problems in RN with critical growth

In this study, a given quasilinear problem is solved using variational methods. In particular, the existence of nontrivial solutions for GP is examined using minimax methods. The main theorem on the existence of a nontrivial solution for GP is detailed.

Critical behavior in a cross-situational lexicon learning scenario

The associationist account for early word learning is based on the co-occurrence between referents and words. Here we introduce a noisy cross-situational learning scenario in which the referent of the uttered word is eliminated from the context with probability gamma, thus modeling the noise produced by out-of-context words. We examine the performance of a simple associative learning algorithm and find a critical value of the noise parameter gamma(c) above which learning is impossible. We use finite-size scaling to show that the sharpness of the transition persists across a region of order tau(-1/2) about gamma(c), where tau is the number of learning trials, as well as to obtain the learning error (scaling function) in the critical region. In addition, we show that the distribution of durations of periods when the learning error is zero is a power law with exponent -3/2 at the critical point. Copyright (C) EPLA, 2012

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

Mean-Field critical behavior and ergodicity break in a nonequilibrium one-dimensional RSOS growth model

We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical Ginzburg-Landau scenario for the phase transition of the model, and estimates of the "magnetic" exponent seem to confirm its mean-field critical behavior. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behavior as the original model. Our results support the usefulness of off-critical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in the appendix a good and simple pseudo-random number generator used in our simulations.

Critical transport properties of random metals in large magnetic fields

The threshold behavior of the transport properties of a random metal in the critical region near a metal–insulator transition is strongly affected by the measuring electromagnetic fields. In spite of the randomness, the electrical conductivity exhibits striking phase-coherent effects due to broken symmetry, which greatly sharpen the transition compared with the predictions of effective medium theories, as previously explained for electrical conductivities. Here broken symmetry explains the sign reversal of the T → 0 magnetoconductance of the metal–insulator transition in Si(B,P), also previously not understood by effective medium theories. Finally, the symmetry-breaking features of quantum percolation theory explain the unexpectedly very small electrical conductivity temperature exponent α = 0.22(2) recently observed in Ni(S,Se)2 alloys at the antiferromagnetic metal–insulator transition below T = 0.8 K.

Critical behavior of the dilute antiferromagnet in a magnetic field

We study the critical behavior of the diluted antiferromagnet in a field with the tethered Monte Carlo formalism. We compute the critical exponents (including the elusive hyperscaling violations exponent θ). Our results provide a comprehensive description of the phase transition and clarify the inconsistencies between previous experimental and theoretical work. To do so, our method addresses the usual problems of numerical work (large tunneling barriers and self-averaging violations).

Nonequilibrium critical scaling from quantum thermodynamics

The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully predicts the equilibrium critical exponents for the crossover length and the order parameter of the model, and, moreover, implies a new exponent for the rescaled irreversible work. By connecting the irreversible work to the two-impurity spin correlation function, our findings can be tested experimentally.