Short-time dynamics of a family of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math>noncollinear magnets

Bekhechi, S.; Southern, B. W.; Peles, Amra; Mouhanna, D.

doi:10.1103/physreve.74.016109

Cited by 19 publications

(19 citation statements)

References 24 publications

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“…Both phenomena should not occur at the second order phase transition. Recent numerical simulations give evidence of the first order phase transition for frustrated systems [57][58][59][60][61]. The RG investigations based on the ε-and pseudo-ε-expansions [11,16,17] indicate the absence of the second order phase transition within φ 4 theory for a frustrated model at physical values N = 2 and N = 3.…”

Section: Discussionmentioning

confidence: 99%

Analysis of the 3d massive renormalization group perturbative expansions: a delicate case

Delamotte¹,

Dudka²,

Holovatch³

et al. 2010

Condens. Matter Phys.

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The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N ) model, the cubic model and the antiferromagnetic model defined on the stacked triangular lattice. We consider all models at fixed d = 3 and analyze the resummation procedures currently used to compute the critical exponents. We first show that, for the O(N ) model, the resummation does not eliminate all non-physical (spurious) fixed points (FPs). Then the dependence of spurious as well as of the Wilson-Fisher FPs on the resummation parameters is carefully studied. The critical exponents at the Wilson-Fisher FP show a weak dependence on the resummation parameters. On the contrary, the exponents at the spurious FP as well as its very existence are strongly dependent on these parameters. For the cubic model, a new stable FP is found and its properties depend also strongly on the resummation parameters. It appears to be spurious, as expected. As for the frustrated models, there are two cases depending on the value of the number of spin components. When N is greater than a critical value Nc, the stable FP shows common characteristic with the Wilson-Fisher FP. On the contrary, for N < Nc, the results obtained at the stable FP are similar to those obtained at the spurious FPs of the O(N ) and cubic models. We conclude from this analysis that the stable FP found for N < Nc in frustrated models is spurious. Since Nc > 3, we conclude that the transitions for XY and Heisenberg frustrated magnets are of first order.

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Section: Discussionmentioning

confidence: 99%

Analysis of the 3d massive renormalization group perturbative expansions: a delicate case

Delamotte¹,

Dudka²,

Holovatch³

et al. 2010

Condens. Matter Phys.

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“…1 for details͒, several points of the physics of frustrated magnets remain controversial. The first one is that, although the occurrence of ͑weak͒ first-order transitions is by now well established in several three-dimensional systems, [19][20][21][22][23][24][25][26][27] this does not imply that all systems, sharing the same order parameter and the same symmetries, undergo first-order phase transitions ͑see, for instance, Ref. 28 for a recent numerical computation where a second-order phase transition is observed͒.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, other experiments as well as extensive Monte Carlo simulations performed on STAs or on similar models have exhibited weak first-order behavior. [19][20][21][22][23][24][25][26][27] Two main explanations have been proposed to describe these contradicting results.…”

Section: Introductionmentioning

confidence: 99%

Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

et al. 2010

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We show that the critical behavior of two-and three-dimensional frustrated magnets cannot reliably be described from the known five-and six-loop perturbative renormalization-group results. Our conclusions are based on a careful reanalysis of the resummed perturbative series obtained within the zero-momentum massive scheme. In three dimensions, the critical exponents for XY and Heisenberg spins display strong dependences on the parameters of the resummation procedure and on the loop order. This behavior strongly suggests that the fixed points found are in fact spurious. In two dimensions, we find, as in the O͑N͒ case, that there is apparent convergence of the critical exponents but toward erroneous values. As a consequence, the interesting question of the description of the crossover/transition induced by Z 2 topological defects in two-dimensional frustrated Heisenberg spins remains open.

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“…One of the most studied systems is the stacked triangular antiferromagnet (STA) with interaction between NN. This system with Ising [10], XY and Heisenberg spins [11,12] have been intensively studied since 1987 [13,14,15,16,17,18,19,20], but only recently that the 20-year controversy comes to an end [21,22,23,24,25,26,27,28,29,30]. Note that numerical simulations require now new efficient algorithms to deal with frustrated systems [29,30].…”

Section: Introductionmentioning

confidence: 99%

Flat energy-histogram simulation of the phase transition in an Ising fully frustrated lattice

Ngo¹,

Hoang²,

Diep³

2011

J. Phys.: Condens. Matter

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Abstract. We show in this paper the results on the phase transition of the so-called fully frustrated simple cubic lattice with the Ising spin model. We use here the Monte Carlo method with the flat energy-histogram Wang-Landau technique which is very powerful to detect weak first-order phase transition. We show that the phase transition is clearly of first order, providing a definite answer to a question raised 25 years ago.

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Short-time dynamics of a family ofXYnoncollinear magnets

Cited by 19 publications

References 24 publications

Analysis of the 3d massive renormalization group perturbative expansions: a delicate case

Analysis of the 3d massive renormalization group perturbative expansions: a delicate case

Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

Flat energy-histogram simulation of the phase transition in an Ising fully frustrated lattice

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