Correlations in the Ising antiferromagnet on the anisotropic kagome lattice

Apel, W.; Everts, H. U.

doi:10.1088/1742-5468/2011/09/p09002

Cited by 5 publications

(5 citation statements)

References 25 publications

(59 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4 illustrates the usefulness of the reduced susceptibility χ T [46], whose temperature evolution quantitatively describes the successive crossovers between disordered regimes. Last but not least, we hope to bring to light an interesting facet of distorted frustrated magnets, where extended regions of magnetic disorders can be stabilized by anisotropy, such as on the Cairo 71,72 , kagome 51,73 and pyrochlore 74 lattices. Such connection is particularly promising since it expands the possibilities of experimental realizations, for example in Volborthite kagome 75 or breathing pyrochlores 76,77 .…”

Section: Discussionmentioning

confidence: 99%

Reentrance of disorder in the anisotropic shuriken Ising model

2016

View full text Add to dashboard Cite

For a material to order upon cooling is common sense. What is more seldom is for disorder to reappear at lower temperature, which is known as reentrant behavior. Such resurgence of disorder has been observed in a variety of systems, ranging from Rochelle salts to nematic phases in liquid crystals. Frustration is often a key ingredient for reentrance mechanisms. Here we shall study a frustrated model, namely the anisotropic shuriken lattice, which offers a natural setting to explore an extension of the notion of reentrance between magnetic disordered phases. By tuning the anisotropy of the lattice, we open a window in the phase diagram where magnetic disorder prevails down to zero temperature. In this region, the competition between multiple disordered ground states gives rise to a double crossover where both the low- and high-temperature regimes are less correlated than the intervening classical spin liquid. This reentrance of disorder is characterized by an entropy plateau, a multi-step Curie law crossover and a rather complex diffuse scattering in the static structure factor. Those results are confirmed by complementary numerical and analytical methods: Monte Carlo simulations, Husimi-tree calculations and an exact decoration-iteration transformation.Comment: 16 pages, 13 figure

show abstract

Section: Discussionmentioning

confidence: 99%

Reentrance of disorder in the anisotropic shuriken Ising model

2016

View full text Add to dashboard Cite

show abstract

“…An exact result was obtained more recently for the correlation length between middle spins from transfer matrix computations using Toeplitz determinants [47]:…”

Section: A Nearest-neighbor Ising Antiferromagnet In Zero Fieldmentioning

confidence: 98%

“…We start in Sec. III with the nearest-neighbor Ising antiferromagnet on the kagome lattice, which was extensively studied before the present paper [22,23,40,[43][44][45][46][47][48]. We discuss its short-range spin-spin correlations and we compute its correlation length using tensor networks.…”

Section: Introductionmentioning

confidence: 99%

Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small farther-neighbor couplings

et al. 2021

View full text Add to dashboard Cite

Despite their simple formulation, short-range classical antiferromagnetic Ising models on frustrated lattices give rise to exotic phases of matter, in particular, due to their macroscopic ground-state degeneracy. Recent experiments on artificial spin systems comprising arrays of chirally coupled nanomagnets provide a significant strengthening of the nearest-neighbor couplings compared to systems with dipolar-coupled nanomagnets. This opens the way to design artificial spin systems emulating Ising models with nearest-neighbor couplings. In this paper, we compare the results of an extensive investigation with tensor network and Monte Carlo simulations of the nearest-and farther-neighbor (J 1 − J 2 − J 3|| ) kagome Ising antiferromagnet with the experimental spinspin correlations of a kagome lattice of chirally coupled nanomagnets. Even though the ratios between the farther-neighbor couplings and the nearest-neighbor coupling estimated from micromagnetic simulations are much smaller than for dipolar-coupled nanomagnets, we show that they still play an essential role in the selection of the correlations.

show abstract

“…While the former has a critical point at T = 0, with algebraically decaying spin-spin correlations, the latter has exponentially decaying correlations with a very short correlation length ξ = 1.2506 [6,7]. One generally assumes that the presence of a macroscopic degeneracy in the ground state of frustrated classical models is highly sensitive to perturbations.…”

Section: Introductionmentioning

confidence: 99%

Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice

Colbois,

Vanhecke,

Vanderstraeten

et al. 2022

Preprint

View full text Add to dashboard Cite

Motivated by dipolar-coupled artificial spin systems, we present a theoretical study of the classical J1 − J2 − J3 Ising antiferromagnet on the kagome lattice. We establish the ground-state phase diagram of this model for J1 > |J2|, |J3| based on exact results for the ground-state energies. When all the couplings are antiferromagnetic, the model has three macroscopically degenerate groundstate phases, and using tensor networks, we can calculate the entropies of these phases and of their boundaries very accurately. In two cases, the entropy appears to be a fraction of that of the triangular lattice Ising antiferromagnet, and we provide analytical arguments to support this observation. We also notice that, surprisingly enough, the dipolar ground state is not a ground state of the truncated model, but of the model with smaller J3 interactions, an indication of a very strong competition between low-energy states in this model.

show abstract

Correlations in the Ising antiferromagnet on the anisotropic kagome lattice

Cited by 5 publications

References 25 publications

Reentrance of disorder in the anisotropic shuriken Ising model

Reentrance of disorder in the anisotropic shuriken Ising model

Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small farther-neighbor couplings

Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice

Contact Info

Product

Resources

About