Computer-simulation study of a disordered classical Heisenberg system in two dimensions with long-range isotropic ferromagnetic interactions

Romano, S.

doi:10.1103/physrevb.46.5420

Cited by 16 publications

(8 citation statements)

References 39 publications

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“…In this work we have applied the SDM, within the framework of the classical statistical mechanics (CSDM), to study the thermodynamic properties of a The rich scenario here obtained in a unified and consistent way for a nontrivial spin model, shows clearly the potentiality and the effectiveness of the SDM also in treating classical many-body systems. It is indeed relevant feature that, already to the lowest-order approximation, the CSDM is able to capture the essential physics of the model, consistent with Monte Carlo simulations [18,28,29] and exact results [20,21,22,23,24], and to obtain results beyond the Tyablikov-like approximation for arbitrary values of dimensionality d and the decaying exponent p > d. Besides, it offers the possibility to achieve systematically higher-order approximations with the aim to improve the results here obtained and to study also the damping of the oscillations on the same footing [6].…”

Section: Discussionsupporting

confidence: 69%

“…The available rigorous results [20,21,22] suggest orientational disorder at all finite temperatures when p ≥ 2d, but no theorem exists entailing existence or absence of LRO for d < p < 2d. Monte Carlo simulations have been also performed for both d(= 1, 2)-dimensional classical FM (for p = 2d [28]) and AFM (for p = 3/2 and p = 3 with d = 1 and d = 2 respectively [29]) Heisenberg long-range models. The results confirm that FM-LRO survives at finite temperature provided d < p < 2d and allow to conjecture that no AFM-LRO exists at all finite temperatures for p > d. Spin-wave studies [29] agree with last conjecture but no definitive statement can be drawn at the present stage.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet with long-range interactions via the spectral density method

Cavallo

Cosenza

Cesare

2004

Physica A: Statistical Mechanics and its Applications

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The thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet, with long-range interactions decaying as r −p and in the presence of an external magnetic field, is investigated by means of the spectral density method in the framework of classical statistical mechanics. We find that long-range order exists at finite temperature for d < p < 2d with d ≤ 2 and for p > d with d > 2, consistently with known theorems. Besides, the related critical temperature is determined and a study of the critical properties is performed.Recently, the critical properties at finite temperature of d-dimensional quantum Heisenberg models, with interactions of the type here considered (here often named "long-range spin models") have been studied using microscopic techniques [14,15,16,17] and Monte Carlo simulations [18]. A summary of the known features sounds as follows. The one-and two-dimensional long-range quantum spin-1/2 Heisenberg ferromagnets in absence of an external magnetic field were investigated by Nakano and Takahashi using the so called modified spin-wave theory [14] and the Schwinger-boson mean-field approximation [15]. Further information were derived for the d-dimensional case by means of the EMM for the two-time Green functions using the Tyablikov decoupling procedure [16]. Monte Carlo simulations for the two-dimensional quantum spin-1/2 Heisenberg model have been also performed for 2 < p ≤ 6 [18]. This scenario, has been recently enriched by an extension [17] of the Mermin-Wagner theorem [19] for the existence of ferromagnetic (FM) LRO at finite temperature in quantum Heisenberg and XY models in d(= 1, 2) dimensions with r −p -and oscillatory-interactions.Classical long-range spin-s Heisenberg FM models have attracted great atten-

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Section: Discussionsupporting

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet with long-range interactions via the spectral density method

Cavallo

Cosenza

Cesare

2004

Physica A: Statistical Mechanics and its Applications

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“…For σ < d/2 the critical indices take their MF values, for d/2 < σ < 2 they are σ-dependent, and for σ > 2 they take their short-range (SR) values. Similar investigations have been conducted * Corresponding author: cristian@mda.cinvestav.mx for Potts [13,15,16,17], Heisenberg [18,19,20,21,22,23], and other [24,25] models. The following picture is often found: for small enough decay rate µ, MF indices are obtained.…”

Section: Introductionmentioning

confidence: 56%

Shortest paths on systems with power-law distributed long-range connections

Moukarzel

Menezes

2002

Phys. Rev. E

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We discuss shortest-path lengths ℓ(r) on periodic rings of size L supplemented with an average of pL randomly located long-range links whose lengths are distributed according to P l ∼ l −µ . Using rescaling arguments and numerical simulation on systems of up to 10 7 sites, we show that a characteristic length ξ exists such that ℓ(r) ∼ r for r < ξ but ℓ(r) ∼ r θs (µ) for r >> ξ. For small p we find that the shortest-path length satisfies the scaling relation ℓ(r, µ, p)/ξ = f (µ, r/ξ). Three regions with different asymptotic behaviors are found, respectively: a) µ > 2 where θs = 1, b) 1 < µ < 2 where 0 < θs(µ) < 1/2 and, c) µ < 1 where ℓ(r) behaves logarithmically, i.e. θs = 0. The characteristic length ξ is of the form ξ ∼ p −ν with ν = 1/(2 − µ) in region b), but depends on L as well in region c). A directed model of shortest-paths is solved and compared with numerical results.

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“…We obviously cannot claim any comparable accuracy, and simply use the results obtained at T * = 1.5 as crude estimates for the behavior of the correlation function at transition; model H4 may also support a BKTLT, whose transition temperature was estimated to be 1.440 ± 0.005. 36 …”

Section: Resultsmentioning

confidence: 99%

Computer Simulation Study of Classical Spin Models in Two Dimensions with Long-Range Ferromagnetic Interactions Anisotropic in Spin Space

Romano

Zagrebnov

1998

Int. J. Mod. Phys. B

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We have considered a classical spin system, consisting of 3-component unit vectors, associated with a two-dimensional lattice {u k , k ∈ Z 2 }, and interacting via a translationally invariant pair potential, of the long-range ferromagnetic form, anisotropic in spin spacehere a ≥ 0, b ≥ 0, σ > 2, is a positive constant setting energy and temperature scales (i.e. T * = k B T / ), x j denotes dimensionless coordinates of lattice sites, and u j,α cartesian spin components; our discussion has been specialized to the extreme, O(2)symmetric, case 0 = a < b. When 2 < σ < 4, the potential model can be proven to support an ordering transition taking place at finite temperature; on the other hand, when σ ≥ 4 a Berezinskiǐ-Kosterlitz-Thouless-like transition takes place. Two potential models defined by σ = 3 and σ = 4, respectively, have been characterized quantitatively by Monte Carlo simulation. For σ = 3, comparison is also reported with other theoretical treatments, such as Molecular Field and Two Site Cluster approximations.PACS number(s): 05.50, 75.10 *

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Computer-simulation study of a disordered classical Heisenberg system in two dimensions with long-range isotropic ferromagnetic interactions

Cited by 16 publications

References 39 publications

Thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet with long-range interactions via the spectral density method

Thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet with long-range interactions via the spectral density method

Shortest paths on systems with power-law distributed long-range connections

Computer Simulation Study of Classical Spin Models in Two Dimensions with Long-Range Ferromagnetic Interactions Anisotropic in Spin Space

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