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.

We present a field-theoretical treatment of the critical behavior of three-dimensional weakly diluted quenched Ising model. To this end we analyse in the replica limit n → 0 the 5-loop renormalization group functions of the φ 4 -theory with O(n)-symmetric and cubic interactions (H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B 342, 284 (1995)). The minimal subtraction scheme allows one to develop either the √ ε-expansion series or to proceed within 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. We report resummed numerical values for the effective and asymptotic critical exponents. The results obtained within the 3d approach agree pretty well with recent Monte Carlo simulations. √ ε-expansion does not allow reliable estimates for d = 3.

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Six-loop massive scheme renormalization group functions of a d = 3-dimensional cubic model (J. M. Carmona, A. Pelissetto, and E. Vicari, Phys. Rev. B 61, 15136 (2000)) are reconsidered by means of the pseudo-ε expansion. The marginal order parameter components number Nc = 2.862 ± 0.005 as well as critical exponents of the cubic model are obtained. Our estimate Nc < 3 leads in particular to the conclusion that all ferromagnetic cubic crystals with three easy axis should undergo a first order phase transition.

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