<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XY</mml:mi></mml:math>frustrated systems: Continuous exponents in discontinuous phase transitions

Tissier, Matthieu; Delamotte, Bertrand; Mouhanna, D.

doi:10.1103/physrevb.67.134422

Cited by 50 publications

(88 citation statements)

References 42 publications

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“…Finally at N = N c 1 one of the nontrivial FPs merges with the FP H and, with further decrease of N, passes to the quadrant u > 0, v > 0, still remaining unstable. The above picture is supported both by the perturbative RG approach (ε-expansion accompanied by subsequent resummation [14] or by a conjecture about the series behaviour [15], resummed expansion in terms of renormalized couplings in a 3d RG scheme [5,6,13], 1/N expansion [15,16]) and the non-perturbative RG [7,17,18,19].…”

Section: The Model and The Pseudo-ε Expansionmentioning

confidence: 93%

On the criticality of frustrated spin systems with noncollinear order

Holovatch¹,

Ivaneyko²,

Delamotte³

2004

J. Phys. A: Math. Gen.

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Abstract. We analyze the universal features of the critical behaviour of frustrated spin systems with noncollinear order. By means of the field theoretical renormalization group approach, we study the 3d model of a frustrated magnet and obtain pseudo-ε expansions for its universal order parameter marginal dimensions. These dimensions govern accessibility of the renormalization group transformation fixed points, and, hence, define the scenario of the phase transition.

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Section: The Model and The Pseudo-ε Expansionmentioning

confidence: 93%

On the criticality of frustrated spin systems with noncollinear order

Holovatch¹,

Ivaneyko²,

Delamotte³

2004

J. Phys. A: Math. Gen.

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“…We do not give the details here. We now introduce the dimensionless renormalized quantities defined as: (153) as well as the threshold functions which are defined and discussed in Appendix C. We then get the following flow equations [118]:…”

Section: The T-derivation and The Flow Equationsmentioning

confidence: 99%

“…From this point of view, the study of frustrated magnets has been rather disappointing, the experimental and numerical contexts excluding such an hypothesis. At the same time, the phenomenology of frustrated magnets has displayed a novel kind of critical behavior -generic scaling without universality [118] -requiring the use of new theoretical approaches.…”

Section: Conclusion and Prospectsmentioning

confidence: 99%

Nonperturbative renormalization-group approach to frustrated magnets

2004

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This article is devoted to the study of the critical properties of classical XY and Heisenberg frustrated magnets in three dimensions. We first analyze the experimental and numerical situations. We show that the unusual behaviors encountered in these systems, typically nonuniversal scaling, are hardly compatible with the hypothesis of a second order phase transition. Moreover, the fact that the scaling laws are significantly violated and that the anomalous dimension is negative in many cases provides strong indications that the transitions in frustrated magnets are most probably of very weak first order. We then review the various perturbative and early nonperturbative approaches used to investigate these systems. We argue that none of them provides a completely satisfactory description of the three-dimensional critical behavior. We then recall the principles of the nonperturbative approach -the effective average action method -that we have used to investigate the physics of frustrated magnets. First, we recall the treatment of the unfrustrated -O(N ) -case with this method. This allows to introduce its technical aspects. Then, we show how this method unables to clarify most of the problems encountered in the previous theoretical descriptions of frustrated magnets. Firstly, we get an explanation of the long-standing mismatch between different perturbative approaches which consists in a nonperturbative mechanism of annihilation of fixed points between two and three dimensions. Secondly, we get a coherent picture of the physics of frustrated magnets in qualitative and (semi-) quantitative agreement with the numerical and experimental results. The central feature that emerges from our approach is the existence of scaling behaviors without fixed or pseudo-fixed point and that relies on a slowing-down of the renormalization group flow in a whole region in the coupling constants space. This phenomenon allows to explain the occurence of generic weak first order behaviors and to understand the absence of universality in the critical behavior of frustrated magnets.

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“…A remarkable example is given by the three dimensional frustrated spin systems, either the triangular antiferromagnets or the helimagnets. Here, the results obtained by means of the resummed perturbation series and those obtained from the NPRG are qualitatively different [8][9][10][11][12][13]. The former predicts a second order phase transition whereas the latter very weakly predicts first order transitions.…”

Section: Some Results Obtained With the Nprg Methodsmentioning

confidence: 91%

“…Second, even in cases where five or six loop series are known, resummations do not always lead to converged results. This is the case, for instance, for frustrated spin systems in three dimensions [8][9][10][11][12][13]. Again, contrary to the common belief, the problem is not just to compute accurately critical exponents but to determine the qualitative behavior of the system at the transition: either first or second order phase transition, belonging or not to a given universality class, etc.…”

Section: Introductionmentioning

confidence: 99%

What can be learnt from the nonperturbative renormalization group?

Delamotte¹,

Canet²

2005

Condens. Matter Phys.

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We point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non-perturbative renormalization group formalism is a promising candidate to overcome some of them. We present some results recently obtained in the literature that substantiate our claims. We finally list some open issues for which this formalism could be useful and also review some of its drawbacks.

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XYfrustrated systems: Continuous exponents in discontinuous phase transitions

Cited by 50 publications

References 42 publications

On the criticality of frustrated spin systems with noncollinear order

On the criticality of frustrated spin systems with noncollinear order

Nonperturbative renormalization-group approach to frustrated magnets

What can be learnt from the nonperturbative renormalization group?

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