Cuccoli, Tognetti, Vaia, and Verrucchi Reply:

Cuccoli, Alessandro; Tognetti, V.; Vaia, Ruggero; Verrucchi, Paola

doi:10.1103/physrevlett.79.1584

Cited by 144 publications

(346 citation statements)

References 8 publications

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“…In Fig.5 we show the correlation length and also report the curve for the isotropic model 12 : we notice that the µ = 0.9942 curve lays on the isotropic one up to correlation lengths of the order of 20 lattice spacings (i.e. t ≃ 1.03t c ), while for µ = 0.7 a deviation is evident already for ξ ≃ 2 (i.e.…”

Section: Fig 2 Specific Heat Vs T (Lines and Inset As Inmentioning

confidence: 99%

“…12 and there shown to be the most appropriate to study the isotropic model. The difference between such version and the original one described in Sec.II consists in the appearance of the renormalization parameters κ 2 ,⊥ , instead of θ 2 ,⊥ , in Eqs.…”

Section: Comparison With Experimental Datamentioning

confidence: 99%

“…Different theoretical methods [7][8][9][10][11][12] have been used to examine the rich reservoir of experimental data and the picture of the subject is now well focused, albeit with some shaded parts. In particular open questions still exist [13][14][15][16] on the low-temperature region, where the spin correlation length becomes of the order of 10 2 lattice spacings and the real magnets are seen to develop macroscopic areas of correlated spins.…”

Section: Introductionmentioning

confidence: 99%

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Finite-temperature ordering in two-dimensional magnets

et al. 2000

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We study the two dimensional quantum Heisenberg antiferromagnet on the square lattice with easyaxis exchange anisotropy. By the semiclassical method called pure-quantum self-consistent harmonic approximation we analyse several thermodynamic quantities and investigate the existence of a finite temperature transition, possibly describing the low-temperature critical behaviour experimentally observed in many layered real compounds. We find that an Ising-like transition characterizes the model even when the anisotropy is of the order of 10 −2 J (J being the intra-layer exchange integral), as in most experimental situations. On the other hand, typical features of the isotropic Heisenberg model are observed for both values of anisotropy considered, one in the quasi-isotropic limit and the other in a more markedly easy-axis region. The good agreement found between our theoretical results and the experimental data relative to the real compound Rb2MnF4 shows that the insertion of the easy-axis exchange anisotropy, with quantum effects properly taken into account, provides a quantitative description and explanation of the experimental data, thus allowing to recognize in such anisotropy the main agent for the observed onset of finite temperature long-range order.

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Section: Fig 2 Specific Heat Vs T (Lines and Inset As Inmentioning

confidence: 99%

Section: Comparison With Experimental Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite-temperature ordering in two-dimensional magnets

et al. 2000

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“…(14) and (16) is remarkable, given the fact that the PQSCHA is a completely different method from that used by Hasenfratz. However, the PQSCHA fails to describe the regime of very low-T , e.g., for S=1/2 it holds only for T > ∼ 0.2 J [5,7,15]. In particular, the PQSCHA has been criticized because the expression Eq.…”

mentioning

confidence: 99%

“…In particular, we find that Eq. (1), besides being the outcome of the semiclassical pure-quantum self-consistent harmonic approximation (PQSCHA) [5], remarkably holds also for the quantum field-theoretical prediction [6], as recently improved by Hasenfratz [7]. On the other hand, we show that the PQSCHA, when properly designed to such purpose, allows for a correct description of the low-T regime, via the appearance of the very same J eff (T, S) implicitly entering Hasenfratz's expression.…”

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Quantum two-dimensional Heisenberg antiferromagnet: Bridging the gap between field-theoretical and semiclassical approaches

et al. 2003

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The field-theoretical result for the low-T behaviour of the correlation length of the quantum Heisenberg antiferromagnet on the square lattice was recently improved by Hasenfratz [Eur. Phys. J. B 13, 11 (2000)], who corrected for cutoff effects. We show that starting from his expression, and exploiting our knowledge of the classical thermodynamics of the model, it is possible to take into account non-linear effects which are responsible for the main features of the correlation length at intermediate temperature. Moreover, we find that cutoff effects lead to the appearance of an effective exchange integral depending on the very same renormalization coefficients derived in the framework of the semiclassical pure-quantum self-consistent harmonic approximation: The gap between quantum field-theoretical and semiclassical results is here eventually bridged.PACS numbers: 05.50.+q, 75.10.Jm In the last two decades, thermodynamic properties of the quantum Heisenberg antiferromagnet on the squarelattice (QHAF) have been determined by a number of substantially different methods. Theoretical predictions were compared with experimental data for real compounds [1], as well as with numerical simulations obtained by different methods [2,3], and also with high-T series expansions [4]. Despite this effort, however, a comprehensive picture of the subject has not yet been formulated.Much of the analysis and debate on the QHAF has focused on the temperature-and spin-dependence of the staggered correlation length ξ(T, S). Goal of this paper is to show that ξ(T, S) can be expressed aswhere the effective exchange integral J eff (T, S) embodies quantum effects and is defined in terms of purely quantum spin-fluctuations, while ξ cl (T /J cl ) is the correlation length of the classical HAF. In particular, we find that Eq. (1), besides being the outcome of the semiclassical pure-quantum self-consistent harmonic approximation (PQSCHA) [5], remarkably holds also for the quantum field-theoretical prediction [6], as recently improved by Hasenfratz [7]. On the other hand, we show that the PQSCHA, when properly designed to such purpose, allows for a correct description of the low-T regime, via the appearance of the very same J eff (T, S) implicitly entering Hasenfratz's expression. It is a definite suprise that a typical semiclassical expression such as Eq. (1), come out of a field-theoretical result, especially in the case of the QHAF, where semiclassical and field-theoretical approaches seemed destined to describe different regions of the (T, S) plane, with no possible overlap.The QHAF is defined by the spin Hamiltonianwhere J>0, i=(i 1 , i 2 ), d=(±1, ±1), and lengths are in lattice units; the spinThe correlation length ξ(T, S) is defined via the asymptotic behaviour, lim |r|→∞ G(r) ∝ e −|r|/ξ , of the staggered correlation function G(r)≡(−1) r1+r2 Ŝ z iŜ z i+r , with r=(r 1 , r 2 ) any vector on the square lattice.The classical counterpart of the QHAF corresponds to the limit S→∞ with JS 2 →J cl , that gives the classical Hamiltonian H=...

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Quantum phase diagram for homogeneous Bose-Einstein condensate

Kleinert

Schmidt

Pelster³

2005

Ann. Phys.

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We calculate the quantum phase transition for a homogeneous Bose gas in the plane of s-wave scattering length as and temperature T . This is done by improving a one-loop result near the interaction-free Bose-Einstein critical temperature T (0) c with the help of recent high-loop results on the shift of the critical temperature due to a weak atomic repulsion using variational perturbation theory. The quantum phase diagram shows a nose above T (0) c , so that we predict the existence of a reentrant transition above T (0) c , where an increasing repulsion leads to the formation of a condensate.

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Cuccoli, Tognetti, Vaia, and Verrucchi Reply:

Cited by 144 publications

References 8 publications

Finite-temperature ordering in two-dimensional magnets

Finite-temperature ordering in two-dimensional magnets

Quantum two-dimensional Heisenberg antiferromagnet: Bridging the gap between field-theoretical and semiclassical approaches

Quantum phase diagram for homogeneous Bose-Einstein condensate

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