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Register a new userAnisotropic XY antiferromagnets in a field
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Classical anisotropic XY antiferromagnets in a field on square and simple cubic lattices are studied using mainly Monte Carlo simulations. While in two dimensions the ordered antiferromagnetic and spin--flop phases are observed to be separated by a narrow disordered phase, a line of direct transitions of first order between the two phases and a bicritical point are found in three dimensions. Results are compared to previous findings.
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We use numerical transfer-matrix methods, together with finite-size scaling and conformal invariance concepts, to discuss critical properties of two-dimensional honeycomb-lattice Ising spin-1/2 magnets, with couplings which are antiferromagnetic along at least one lattice axis, in a uniform external field. We focus mainly on the shape of the phase diagram in field-temperature parameter space; in order to do so, both the order and universality class of the underlying phase transition are examined. Our results indicate that, in one particular case studied, the critical line has a horizontal section (i.e. at constant field) of finite length, starting at the zero-temperature end of the phase boundary. Other than that, we find no evidence of unusual behavior, at variance with the reentrant features predicted in earlier studies.
We study systems of classical magnetic dipoles on simple cubic lattices with dipolar and antiferromagnetic exchange interactions. By analysis and Monte Carlo (MC) simulations, we find how the antiferromagnetic phases vary with uniaxial and fourfold anisotropy constants, C and D, as well as with exchange strength J. We pay special attention to the spin reorientation (SR) phase, and exhibit in detail the nature of its broken symmetries. By mean field theory and by MC, we also obtain the ratio of the higher ordering temperature to the SR transition temperature, and show that it depends mainly on D/C, and rather weakly on J. We find a reverse SR transition.
We study classical and quantum Heisenberg antiferromagnets with exchange anisotropy of XXZ-type and crystal field single-ion terms of quadratic and cubic form in a field. The magnets display a variety of phases, including the spin-flop (or, in the quantum case, spin-liquid) and biconical (corresponding, in the quantum lattice gas description, to supersolid) phases. Applying ground-state considerations, Monte Carlo and density matrix renormalization group methods, the impact of quantum effects and lattice dimension is analysed. Interesting critical and multicritical behaviour may occur at quantum and thermal phase transitions.
The correlation functions of certain $n$-cluster XY models are explicitly expressed in terms of those of the standard Ising chain in transverse field.
Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the strongest cases presented has been for the pyrochlore XY antiferromagnet Er2Ti2O7, with the ground state selection proceeding by order by disorder induced through the effects of quantum fluctuations. This identification assumes the smallness of the effect of virtual crystal field fluctuations that could provide an alternative route to picking the ground state. Here we show that this order by virtual crystal field fluctuations is not only significant, but competitive with the effects of quantum fluctuations. Further, we argue that higher-multipolar interactions that are generically present in rare-earth magnets can dramatically enhance this effect. From a simplified bilinear-biquadratic model of these multipolar interactions, we show how the virtual crystal field fluctuations manifest in Er2Ti2O7 using a combination of strong coupling perturbation theory and the random phase approximation. We find that the experimentally observed psi2 state is indeed selected and the experimentally measured excitation gap can be reproduced when the bilinear and biquadratic couplings are comparable while maintaining agreement with the entire experimental spin-wave excitation spectrum. Finally, we comments on possible tests of this scenario and discuss implications for other order-by-disorder candidates in rare-earth magnets.
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