Field Critical Behavior Research Articles

Magnetism of powder samples and of single crystals

The temperature dependence of the magnetic order parameter of NiF2, MnCO3 and K2NiF4 measured on powder samples is compared with data obtained on single crystals. It is found that the dynamic dimensionality of the NiF2 and MnCO3 powder samples is one-dimensional (1D) for all temperatures T<TN. This shows that the powder grains are mono-domain particles. In the multi-domain single crystals isotropic 3D dynamic symmetry is observed. In order to explain isotropy in the bulk single crystals a dynamic averaging process over all domain orientations has to be postulated. For single crystal material of K2NiF4 a critical exponent of β=0.14±0.01 has been reported. Our neutron diffraction measurements on powder material yield to a very good approximation mean field critical behaviour indicating isotropic dynamics in the critical range. This unexpected result points to a dynamic averaging process over all differently oriented powder grains. As we have argued earlier, the observed universality in the dynamics of ordered magnets is due to a boson guiding field. Averaging over all powder grains, requests that the mean free path of the field bosons is larger than the size of the grains. Additionally, it must be assumed that the field quanta are able to tunnel across the interface between adjacent grains. In polycrystalline bulk samples of the 2D ferromagnet Rb2CrCl4 and of the 1D antiferromagnet KCuF3 also mean field critical behaviour is identified. As a consequence, a similar averaging process as in the K2NiF4 powder sample can be assumed to average over the mosaic structure of polycrystalline bulk material of Rb2CrCl4 and KCuF3. High quality single crystals of Rb2CrCl4 and of KCuF3 exhibit critical exponent of β~0.3. Dependence of the critical exponents on the mesoscopic morphology of the sample is considered as a typical indication of a boson controlled dynamics, and may partly explain the surprisingly broad distribution of critical exponent values reported in literature.

FIBERS ON A GRAPH WITH LOCAL LOAD SHARING

We study a random fiber bundle model with tips of the fibers placed on a graph having co-ordination number 3. These fibers follow local load sharing with uniformly distributed threshold strengths of the fibers. We have studied the critical behavior of the model numerically using a finite size scaling method and the mean field critical behavior is established. The avalanche size distribution is also found to exhibit a mean field nature in the asymptotic limit.

Lattice model of equilibrium polymerization. V. Scattering properties and the width of the critical regime for phase separation

Dynamic clustering associated with self-assembly in many complex fluids can qualitatively alter the shape of phase boundaries and produce large changes in the scale of critical fluctuations that are difficult to comprehend within the existing framework of theories of critical phenomena for nonassociating fluids. In order to elucidate the scattering and critical properties of associating fluids, we consider several models of equilibrium polymerization that describe widely occurring types of associating fluids at equilibrium and that exhibit the well defined cluster geometry of linear polymer chains. Specifically, a Flory-Huggins-type lattice theory is used, in conjunction with the random phase approximation, to compute the correlation length amplitude xi(o) and the Ginzburg number Gi corresponding, respectively, to the scale of composition fluctuations and to a parameter characterizing the temperature range over which Ising critical behavior is exhibited. Our calculations indicate that upon increasing the interparticle association energy, the polymer chains become increasingly long in the vicinity of the critical point, leading naturally to a more asymmetric phase boundary. This increase in the average degree of polymerization implies, in turn, a larger xi(o) and a drastically reduced width of the critical region (as measured by Gi). We thus obtain insight into the common appearance of asymmetric phase boundaries in a wide range of "complex" fluids and into the observation of apparent mean field critical behavior even rather close to the critical point.

Monte Carlo simulations of a compressible Ising ferromagnet at constant volume

Compressible Ising models have long been of interest because of the question of how the transition is influenced by elastic degrees of freedom. A careful Monte Carlo study showed, somewhat surprisingly, that an Ising ferromagnet at constant pressure had mean field critical behavior. Subsequently, a theoretical investigation predicted that the effect of elastic interactions depends upon whether the pressure or the volume is held fixed. We have now performed extensive Monte Carlo simulations of a compressible Ising ferromagnet at constant volume and determined the phase diagram as a function of applied magnetic field. In contrast to theoretical predictions, we find a single phase boundary that is first order everywhere except at single point where d T / d H = 0 . Unusual, slab-like structures are found in the “ordered” phase, and visualization played a crucial role in elucidating the physical behavior.

Crossover from classical to random-field critical exponents in As-dopedTbVO4

Using birefringence techniques we have measured the critical exponents beta, gamma, and delta in As-doped TbVO4, a structural realization of the random-field Ising model where random strain fields are introduced by V-As size mismatch. For pure TbVO4 we observe the expected classical critical exponents, while for a mixed sample with 15% As concentration our results are beta=0.31 +/-0.03, gamma=1.22 +/-0.07, and delta=4.2 +/-0.7. These values are consistent with the critical exponents for the short range pure Ising model in three dimensions in agreement with a prediction by Toh. The susceptibility data showed a crossover with temperature from classical to random field critical behaviour.

Quantum critical behavior of itinerant ferromagnets

AbstractWe investigate the quantum phase transition of itinerant ferromagnets. It is shown that correlation effects in the underlying itinerant electron system lead to singularities in the order parameter field theory that result in an effective long‐range interaction between the spin fluctuations. This interaction turns out to be generically antiferromagnetic for clean systems. In disordered systems analogous correlation effects lead to even stronger singularities. The resulting long‐range interaction is, however, generically ferromagnetic.We discuss two possibilities for the ferromagnetic quantum phase transition. In clean systems, the transition is generically of first order, as is experimentally observed in MnSi. However, under certain conditions the transition may be continuous with non‐mean field critical behavior. In disordered systems, one finds a very rich phase diagram showing first order and continuous phase transitions and several multicritical points.

Quantum critical behavior of itinerant ferromagnets

We investigate the quantum phase transition of itinerant ferromagnets. It is shown that correlation effects in the underlying itinerant electron system lead to singularities in the order parameter field theory that result in an effective long-range interaction between the spin fluctuations. This interaction turns out to be generically {\em antiferromagnetic} for clean systems. In disordered systems analogous correlation effects lead to even stronger singularities. The resulting long-range interaction is, however, generically ferromagnetic. We discuss two possibilities for the ferromagnetic quantum phase transition. In clean systems, the transition is generically of first order, as is experimentally observed in MnSi. However, under certain conditions the transition may be continuous with non-mean field critical behavior. In disordered systems, one finds a very rich phase diagram showing first order and continuous phase transitions and several multicritical points.

Mean field critical behaviour for the frustrated percolation model

We give a mean field analysis for a fully frustrated (2 s)-state spin model that includes Ising and Potts variables. This model has been extensively used in recent years to study the frustrated percolation and the glassy transition. In fact it exhibits a percolation transition T p and a second thermal transition at an equal or lower temperature T c .

Monte Carlo simulation of polymeric materials

Polymeric materials present a major challenge to computer simulation, since they exhibit structure on many different length scales (bond length, 1 Å; coil size, 102 Å; correlation length in mixtures, 103 Å). For a study of collective phenomena, such as unmixing of polymer mixtures and mesophase formation in block copolymers, coarse-grained simplified lattice models hence are used. It is shown that in symmetric polymer mixtures (chain lengths NA = NB = N) the critical temperature follows a simple linear relation, TC(N) = aN + b. The onset of crossover phenomena from Ising to mean field critical behavior is observed, but even for N = 512 chains do not behave fully mean-field-like. Asymmetric mixtures also are considered and the corresponding predictions of Flory-Huggins theory are tested. In block copolymers a pretransitional stretching of the chains is found for both symmetric and asymmetric concentrations and analysed in detail. A density reduction in the interfaces between A and B blocks is found in the ordered phase.

Theory of the Fractional Quantum Hall Effect

A theory of the Fractional Quantum Hall Effect is constructed based on magnetic flux fractionization, which lead to instability of the system against selfcompression. A theorem is proved stating that arbitrary potential fail to lift a specific degeneracy of the Landau level. For the case of 1/3 fractional filling a model 3-particles interaction is constructed breaking the symmetry. The rigid 3-particles wave function plays the role of order parameter. In a BCS type of theory the gap in the single particles spectrum is produced by the 3-particles interaction. The mean field critical behaviour and critical parameters are determined as well as the Ginsburg-Landau equation coefficients. The Hall conductivity is calculated from first principles and its temperature dependence is found. The simultaneous tunneling of 3, 5, 7 etc. electrons and quantum interference effects are predicted.

Experiments on random-ordering field critical behavior in dilute antiferromagnets (invited)

We present experimental results bearing on the random-field problem near the bicritical point (BCP) of antiferromagnetic GdAlO3 with various degrees of dilution: 1) From the phase boundaries near the BCP, a random-field crossover exponent φrf≊1.75 is derived. 2) At random-exchange transitions, the susceptibility χ̄ exhibits a divergence-like peak as in the pure material. At random-field transitions, on the other hand, only a broad maximum of χ̄ is observed, suggesting a specific-heat exponent α&amp;lt;−1. 3) The transition from the antiferromagnetic state to the spinflop state below the bicritical point is qualitatively different from the pure case. 4) In the paramagnetic state above the bicritical point, an additional susceptibility peak is observed, whose intensity increases rapidly with the degree of dilution. These results are compared with current theory on the random-field problem.

Departure from mean field critical behavior in ferroelectric DTGS

Dielectric constant and hysteresis loops measurements have been performed in single crystals of deuterated triglycine sulfate (DTGS) in the vicinity of the transition temperature. In the range 0.02°C < Δ T < 0.60°C deviations from mean field behavior were observed. In the range 1°C < Δ T < 10°C the dielectric constant data fitted mean-field predictions fairly well. Using the experimental (non mean-field) values for the critical exponents in the temperature range closer to T c , the “scaling” equation of state h( x) = ( x 0 + x) β( δ-1) was seen to be fulfilled in a wide range of x = ( ΔT/ T c )/( P/ P 0) 1/ gb below and above T c . The same is true for TGS data, using classical values for the exponents.