Taras Yavors'kii

Dy2Ti2O7 Spin Ice: a Test Case for Emergent Clusters in a Frustrated Magnet

Dy2Ti2O7 is a geometrically frustrated magnetic material with a strongly correlated spin ice regime that extends from 1 K down to as low as 60 mK. The diffuse elastic neutron scattering intensities in the spin ice regime can be remarkably well described by a phenomenological model of weakly interacting hexagonal spin clusters, as invoked in other geometrically frustrated magnets. We present a highly refined microscopic theory of Dy2Ti2O7 that includes long-range dipolar and exchange interactions to third nearest neighbors and which demonstrates that the clusters are purely fictitious in this material. The seeming emergence of composite spin clusters and their associated scattering pattern is instead an indicator of fine-tuning of ancillary correlations within a strongly correlated state.

Neutron scattering investigation of the spin ice state in Dy2Ti2O7

Dy2Ti2O7 has been advanced as an ideal spin ice material. We present a neutron scattering investigation of a single-crystal sample of (Dy2Ti2O7)-Dy-162. The scattering intensity has been mapped in zero applied field in the h,h,l and h,k,0 planes of reciprocal space at temperatures between 0.05 and 20 K. The measured diffuse scattering has been compared with that predicted by the dipolar spin ice model. The comparison is good, except at the Brillouin-zone boundaries where extra scattering appears in the experimental data. It is concluded that the dipolar spin ice model provides a successful basis for understanding Dy2Ti2O7, but that there are issues which remain to be clarified.

Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus

We present a field-theoretical treatment of the critical behavior of three-dimensional weakly diluted quenched Ising model. To this end we analyse in a replica limit n=0 5-loop renormalization group functions of the

\epsilon^{1/2}

\phi^4

-Expansion

-theory with O(n)-symmetric and cubic interactions (H.Kleinert and V.Schulte-Frohlinde, Phys.Lett. B342, 284 (1995)). The minimal subtraction scheme allows to develop either the

WEAK QUENCHED DISORDER AND CRITICALITY: RESUMMATION OF ASYMPTOTIC(?) SERIES

\epsilon^{1/2}

Critical Exponents of the Diluted Ising Model between Dimensions 2 and 4

-expansion series or to proceed in the 3d approach, performing expansions in terms of renormalized couplings. Doing so, we compare both perturbation approaches and discuss their convergence and possible Borel summability. To study the crossover effect we calculate the effective critical exponents providing a local measure for the degree of singularity of different physical quantities in the critical region. We report resummed numerical values for the effective and asymptotic critical exponents. Obtained within the 3d approach results agree pretty well with recent Monte Carlo simulations.

Spin Hamiltonian, Competing Small Energy Scales and Incommensurate Long Range Order in the Highly Frustrated Gd3Ga5O12 Garnet Antiferromagnet

\epsilon^{1/2}

Universality classes of the three-dimensional mn-vector model

-expansion does not allow reliable estimates for d=3.

Critical exponents of a three-dimensional weakly diluted quenched Ising model

In these lectures, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range-correlated random-site disorder, and (iii) random anisotropy. Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of these lectures is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.