Frustrated Heisenberg Magnets: A Nonperturbative Approach (original) (raw)
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Frustrated magnets in three dimensions: a nonperturbative approach
Journal of Physics: Condensed Matter, 2004
Frustrated magnets exhibit unusual critical behaviors: they display scaling laws accompanied by nonuniversal critical exponents. This suggests that these systems generically undergo very weak first order phase transitions. Moreover, the different perturbative approaches used to investigate them are in conflict and fail to correctly reproduce their behavior. Using a nonperturbative approach we explain the mismatch between the different perturbative approaches and account for the nonuniversal scaling observed.
2010
We show that the critical behaviour of two-and three-dimensional frustrated magnets cannot reliably be described from the known five-and six-loops perturbative renormalization group results. Our conclusions are based on a careful re-analysis of the resummed perturbative series obtained within the zero momentum massive scheme. In three dimensions, the critical exponents for XY and Heisenberg spins display strong dependences on the parameters of the resummation procedure and on the loop order. This behaviour strongly suggests that the fixed points found are in fact spurious. In two dimensions, we find, as in the O(N ) case, that there is apparent convergence of the critical exponents but towards erroneous values. As a consequence, the interesting question of the description of the crossover/transition induced by Z2 topological defects in two-dimensional frustrated Heisenberg spins remains open.
Effective Hamiltonians for some highly frustrated magnets
Journal of Physics: Condensed Matter, 2007
In prior work, the authors developed a method of degenerate perturbation theory about the Ising limit to derive an effective Hamiltonian describing quantum fluctuations in a half-polarized magnetization plateau on the pyrochlore lattice. Here, we extend this formulation to an arbitrary lattice of corner sharing simplexes of q sites, at a fraction (q − 2k)/q of the saturation magnetization, with 0 < k < q. We present explicit effective Hamiltonians for the examples of the checkerboard, kagome, and pyrochlore lattices. The consequent ground states in these cases for k = 1 are also discussed.
Interplay of topology and geometry in frustrated two-dimensional Heisenberg magnets
Physical Review B, 2014
We investigate two-dimensional frustrated Heisenberg magnets using non-perturbative renormalization group techniques. These magnets allow for point-like topological defects which are believed to unbind and drive either a crossover or a phase transition which separates a low temperature, spin-wave dominated regime from a high temperature regime where defects are abundant. Our approach can account for the crossover qualitatively and both the temperature dependence of the correlation length as well as a broad but well defined peak in the specific heat are reproduced. We find no signatures of a finite temperature transition and an accompanying diverging length scale. Our analysis is consistent with a rapid crossover driven by topological defects.
2004
Frustrated magnets exhibit unusual critical behaviors: they display scaling laws accompanied by nonuniversal critical exponents. This suggests that these systems generically undergo very weak first order phase transitions. Moreover, the different perturbative approaches used to investigate them are in conflict and fail to correctly reproduce their behavior. Using a nonperturbative approach we explain the mismatch between the different perturbative approaches and account for the nonuniversal scaling observed.
Effective critical behaviour of diluted Heisenberg-like magnets
Journal of Magnetism and Magnetic Materials, 2003
In agreement with the Harris criterion, asymptotic critical exponents of threedimensional (3d) Heisenberg-like magnets are not influenced by weak quenched dilution of non-magnetic component. However, often in the experimental studies of corresponding systems concentration-and temperature-dependent exponents are found with values differing from those of the 3d Heisenberg model. In our study, we use the field-theoretical renormalization group approach to explain this observation and to calculate the effective critical exponents of weakly diluted quenched Heisenberg-like magnet. Being non-universal, these exponents change with distance to the critical point T c as observed experimentally. In the asymptotic limit (at T c) they equal to the critical exponents of the pure 3d Heisenberg magnet as predicted by the Harris criterion.
Universal properties of highly frustrated quantum magnets in strong magnetic fields
Low Temperature Physics, 2007
The purpose of the present paper is twofold. On the one hand, we review some recent studies on the low-temperature strong-field thermodynamic properties of frustrated quantum spin antiferromagnets which admit the so-called localized-magnon eigenstates. On the other hand, we provide some complementary new results. We focus on the linear independence of the localized-magnon states, the estimation of their degeneracy with the help of auxiliary classical lattice-gas models, and the analysis of the contribution of these states to thermodynamics.