Some Results Concerning the Crossover Behavior of Quasi—Two-Dimensional and Quasi—One-Dimensional Systems

Liu, Luke L.; Stanley, H. Eugene

doi:10.1103/physrevlett.29.927

Cited by 74 publications

(19 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1,2 In recent years, a large number of quasi-low dimensional, low-spin, spatially anisotropic materials have been synthesized and their properties investigated in great detail. This has led to a renewed interest in these issues including the role of enhanced quantum fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Specific heat of quasi-two-dimensional antiferromagnetic Heisenberg models with varying interplanar couplings

2003

View full text Add to dashboard Cite

We have used the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method to study the three-dimensional (3D) antiferromagnetic Heisenberg model on cubic lattices with inplane coupling J and varying inter-plane coupling J ⊥ < J. The specific heat curves exhibit a 3D ordering peak as well as a broad maximum arising from short-range 2D order. For J ⊥ ≪ J, there is a clear separation of the two peaks. In the simulations, the contributions to the total specific heat from the ordering across and within the layers can be separated, and this enables us to study in detail the 3D peak around Tc (which otherwise typically is dominated by statistical noise). We find that the peak height decreases with decreasing J ⊥ , becoming nearly linear below J ⊥ = 0.2J. The relevance of these results to the lack of observed specific heat anomaly at the ordering transition of some quasi-2D antiferromagnets is discussed.

show abstract

Section: Introductionmentioning

confidence: 99%

Specific heat of quasi-two-dimensional antiferromagnetic Heisenberg models with varying interplanar couplings

2003

View full text Add to dashboard Cite

show abstract

“…This "chain mean field theory" is also essentially equivalent to the crossover scaling theory of [4,5] as applied to the classical xy model in [6,7]. Now g ∝ T .…”

mentioning

confidence: 99%

On a renormalization group approach to dimensional crossover

Affleck

Halperin

1996

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

A recently proposed renormalization group approach to dimensional crossover in quasi-one-dimensional quantum antiferromagnets is improved and then shown to give identical results, in some cases, to those obtained earlier.Recently, [1] a renormalization group (RG) approach was proposed to study a quasione dimensional quantum antiferromagnet, in which the ratio of inter-chain to intra-chain couplings, R → 0. The approach works equally well for crossover to two or three dimensional behavior. It is based on a non-linear σ-model representation. In D space-time dimensions, using the imaginary time formalism, and rescaling time so that the spin-wave velocity is one, the action is written:Here φ is the unit normalized n-component order parameter. It represents the threecomponent Néel order parameter for the Heisenberg antiferromagnet in (D-1) spatial dimensions at T = 0. Alternatively, it could present a classical n-component magnetic order parameter in D spatial dimensions at finite temperature. Λ is an ultraviolet cut-off and g is the dimensionless coupling constant. In the spin-s quantum antiferromagnet, g ≈ 2/s and increases with frustration. For the classical system, g is proportional to the temperature, T .There are actually two quite distinct cases, corresponding to integer or half-integer spin in the quantum system. For integer spin the (1+1) dimensional system has a finite correlation 1

show abstract

“…We also present exact results for the linear chain and the series results ford = 2 . The rp value of 1.75 is the value for the crossover between the 2 D and the 3 D king models (Liu and Stanley 1972). expectations that lattice anisotropy is irrelevant to critical behaviour since the 1D fixed points are doubly unstable whereas the isotropic fixed point is stable with respect to anisotropy.…”

Section: The Pure Anisotropic Timmentioning

confidence: 98%

Numerical calculations of the optical gain due to short-wavelength transitions of helium-like ions in an optically thin plasma

Borovskii¹,

Zatsarinnyi²,

Kardash³

et al. 1990

Sov. J. Quantum Electron.

View full text Add to dashboard Cite

We study both the pure anisotropic and the anisotropically diluted transverse Ising model at zero temperature on the square lattice. In the former the couplings along each Cartesian direction are allowed to be different, whereas in the latter it is the bond concentration which may be different along the Cartesian directions. By means of a position space renormalisation group scheme, we find that in both cases the isotropic systems are stable with respect to anisotropy perturbations. We also discuss our results in view of r recently proposed criterion for the stability of pure system fixed points with respect to correlated dilution.

show abstract

Some Results Concerning the Crossover Behavior of Quasi—Two-Dimensional and Quasi—One-Dimensional Systems

Cited by 74 publications

References 12 publications

Specific heat of quasi-two-dimensional antiferromagnetic Heisenberg models with varying interplanar couplings

Specific heat of quasi-two-dimensional antiferromagnetic Heisenberg models with varying interplanar couplings

On a renormalization group approach to dimensional crossover

Numerical calculations of the optical gain due to short-wavelength transitions of helium-like ions in an optically thin plasma

Contact Info

Product

Resources

About