Correlations in Frustrated Magnets : Classical and Quantum Aspects

Abstract: In this thesis, we study three different aspects of the physics of frustrated magnets. First, we study the interplay of thermal and quantum fluctuations in the transverse field frustrated Ising model on the triangular lattice. By means of an efficient Monte Carlo method based on a continuous time algorithm, we map out the phase diagram of the model. The unperturbed classical model (i.e. without transverse field) does not show any order at finite temperatures. Adding quantum fluctuations leads to ordering at zero temperature and adding thermal fluctuations leads to unusual melting via an extended intermediate Kosterlitz-Thouless phase.Second, we study the magnetization properties of spin ice in a magnetic field in the [111] direction by a Monte Carlo method and a number of analytical techniques. An efficient Monte Carlo loop algorithm was developed which allows us to simulate the system at low fields with very high accuracy. We also find a giant peak in the entropy at the transition point between two plateaux. This peak is due to the crossing of an extensive number of energy levels at the transition point. The peak is well described quantitatively by a simple Bethe approximation.Third, we study the cooperative paramagnetic correlations in a number of frustrated classical magnets with O(N) symmetry, including pyrochlore, kagome, and triangular lattices, by Monte Carlo and large-N methods. We find that correlations have a dipolar form giving rise to sharp bow-tie shape features in the structure factor. A detailed comparison of the N = 1,3 and N = ? correlation functions has been made. We find that the N = ? correlations reproduce the correlations for finite N with remarkable quantitative accuracy without any fitting parameter. We show that 1/N corrections do not alter the asymptotic behavior of the correlation functions.