Heisenberg frustrated magnets: a nonperturbative approach

Matthieu Tissier, Bertrand Delamotte, D. Mouhanna

Published Jan 1, 2000• 4 citations

Abstract

Frustrated magnets are a notorious example where the usual perturbative methods are in conflict. Using a nonperturbative Wilson-like approach, we get a coherent picture of the physics of Heisenberg frustrated magnets everywhere between $d=2$ and $d=4$. We recover all known perturbative results in a single framework and find the transition to be weakly first order in $d=3$. We compute effective exponents in good agreement with numerical and experimental data.

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OpenAlex

Abstract

d=2

and

d=4

. We recover all known perturbative results in a single framework and find the transition to be weakly first order in

d=3

. We compute effective exponents in good agreement with numerical and experimental data.

Related papers

Frustrated Heisenberg antiferromagnets: Fluctuation-induced first order vs . deconfined quantum criticality

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Recently it was argued that quantum phase transitions can be radically different from classical phase transitions with, as a highlight, the "deconfined critical points" exhibiting fractionalization of quantum numbers due to Berry phase effects. Such transitions are supposed to occur in frustrated (" J 1 - J 2 ") quantum magnets. We have developed a novel renormalization approach for such systems which is fully respecting the underlying lattice structure. According to our findings, another profound phenomenon is around the corner: a fluctuation-induced (order-out-of-disorder) first-order transition. This has to occur for large spin and we conjecture that it is responsible for the weakly first-order behavior recently observed in numerical simulations for frustrated S = 1/2 systems.Recently it was argued that quantum phase transitions can be radically different from classical phase transitions with, as a highlight, the "deconfined critical points" exhibiting fractionalization of quantum numbers due to Berry phase effects. Such transitions are supposed to occur in frustrated (" J 1 - J 2 ") quantum magnets. We have developed a novel renormalization approach for such systems which is fully respecting the underlying lattice structure. According to our findings, another profound phenomenon is around the corner: a fluctuation-induced (order-out-of-disorder) first-order transition. This has to occur for large spin and we conjecture that it is responsible for the weakly first-order behavior recently observed in numerical simulations for frustrated S = 1/2 systems.

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$\mathrm{XY}$ frustrated magnets exhibit an unusual critical behavior: they display scaling laws accompanied by nonuniversal critical exponents and a negative anomalous dimension. This suggests that they undergo weak first-order phase transitions. We show that all perturbative approaches that have been used to investigate $\mathrm{XY}$ frustrated magnets fail to reproduce these features. Using a nonperturbative approach based on the concept of effective average action, we are able to account for this nonuniversal scaling and to describe qualitatively and, to some extent, quantitatively the physics of these systems.$\mathrm{XY}$ frustrated magnets exhibit an unusual critical behavior: they display scaling laws accompanied by nonuniversal critical exponents and a negative anomalous dimension. This suggests that they undergo weak first-order phase transitions. We show that all perturbative approaches that have been used to investigate $\mathrm{XY}$ frustrated magnets fail to reproduce these features. Using a nonperturbative approach based on the concept of effective average action, we are able to account for this nonuniversal scaling and to describe qualitatively and, to some extent, quantitatively the physics of these systems.

arXiv:cond-mat/0107183Physical review. B, Condensed matterApr 24, 200355 citations

d=2

and

d=4

. We recover all known perturbative results in a single framework and find the transition to be weakly first order in

d=3

. We compute effective exponents in good agreement with numerical and experimental data.

J_1

J_2

model, we find a unifying description of the second-order transition between the Néel phase and the paramagnetic phase and the first-order transition between the Néel phase and the columnar phase. Our approach provides explicit results for the renormalized values of the spin stiffness and spin-wave velocity characterizing the low-energy magnons in the Néel phase.

{a}_{0}

and

{a}_{2}

. We provide estimates of $\ensuremath{\nu}$ in

^{87}\mathrm{Rb},^{41}\mathrm{K}

, and

^{7}\mathrm{Li}

atom gases which can be tested experimentally. We argue that pseudoscaling comes from either a crossover phenomenon due to proximity of the O(6) Wilson-Fisher fixed point

(^{87}\mathrm{Rb}

and

^{41}\mathrm{K})

or the existence of two unphysical fixed points (with complex coordinates) which slow down the RG flow

(^{7}\mathrm{Li})

. These unphysical fixed points are a remnant of the chiral and antichiral fixed points that exist in the $\mathrm{O}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{O}(2)$ model when

N

is larger than ${N}_{c}\ensuremath{\simeq}5.3$ (the transition being then second order and controlled by the chiral fixed point). Finally, we discuss a $\mathrm{O}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{O}(2)$ lattice model and show that our results, even though we find the transition to be first order, are compatible with Monte Carlo simulations yielding an apparent second-order transition.

\mathrm{XY}

frustrated magnets exhibit an unusual critical behavior: they display scaling laws accompanied by nonuniversal critical exponents and a negative anomalous dimension. This suggests that they undergo weak first-order phase transitions. We show that all perturbative approaches that have been used to investigate

\mathrm{XY}

frustrated magnets fail to reproduce these features. Using a nonperturbative approach based on the concept of effective average action, we are able to account for this nonuniversal scaling and to describe qualitatively and, to some extent, quantitatively the physics of these systems.