Thermal expansion in the magnetically ordered phases of holmium

Tindall, D. A.; Steinitz, Michael; Plumer, M. L.

doi:10.1088/0305-4608/7/9/005

Cited by 61 publications

(19 citation statements)

References 11 publications

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“…(106). The calculation proceeds in four steps: i) We first define the running coupling constantsρ 0 , u 2 and Z from functional derivatives of the ansatz of Γ k , Eq.…”

Section: The O(n ) Modelmentioning

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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“…(106). The calculation proceeds in four steps: i) We first define the running coupling constantsρ 0 , u 2 and Z from functional derivatives of the ansatz of Γ k , Eq.…”

Section: The O(n ) Modelmentioning

confidence: 99%

Nonperturbative renormalization-group approach to frustrated magnets

2004

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“…As mentioned, a few authors claimed that their experimental data for Ho and Dy were suggestive of a weak first-order transition [11,12]. Probably, first experimental claim that the transition in Ho might be weakly first order was made by Tindal, Steinitz and Plumer based on their thermal expansion measurements of Ho along the a axis [11].…”

Section: First-order Transition?mentioning

confidence: 99%

“…Probably, first experimental claim that the transition in Ho might be weakly first order was made by Tindal, Steinitz and Plumer based on their thermal expansion measurements of Ho along the a axis [11]. These authors observed a jump-like anomaly in the thermal expansivity along the a axis, although no such anomaly was detected along the c axis.…”

Section: First-order Transition?mentioning

confidence: 99%

Untitled

Kawamura¹

1998

J. Phys.: Condens. Matter

341

470

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Recent theoretical and experimental studies on the critical properties of frustrated antiferromagnets with the noncollinear spin order, including stacked-triangular antiferromagnets and helimagnets, are reviewed. Particular emphasis is put on the novel critical and multicritical behaviors exhibited by these magnets, together with an important role played by the 'chirality'. §1. Introduction Phase transitions and critical phenomena have been a central issue of statistical physics for many years. In particular, phase transitions of magnets or of 'spin systems' have attracted special interest. Thanks to extensive theoretical and experimental studies, we now have rather good understanding of the nature of phase transitions of standard ferromagnets and antiferromagnets. By the term 'standard', I mean here regular and unfrustrated magnets without quenched disorder and frustration. They include ferromagnets and unfrustrated antiferromagnets with the collinear spin order.One key notion which emerged through these studies is the notion of universality. According to the universality hypothesis, a variety of continuous (or secondorder) phase transitions can be classified into a small number of universality classes determined by a few basic properties characterizing the system under study, such as the space dimensionality d, the symmetry of the order parameter and the range of interaction. If one is interested only in the so-called universal quantities, such as critical exponents, amplitude ratios and scaled equation of state, various phase transitions should exhibit exactly the same behavior. In the case of standard bulk magnets in three spatial dimensions (d = 3), universality class is basically determined by the number of the spin components, n. Physically, the index n is related to the type of magnetic anisotropy: Namely, n = 1 (Ising), n = 2 (XY ) and n = 3 (Heisenberg) correspond to magnets with easy-axis-type anisotropy, easy-plane-type anisotropy and no anisotropy (isotropic magnets), respectively. The critical properties associated with these n-component O(n) universality classes have been extensively studied and are now rather well understood. From the renormalization-group (RG) viewpoint, these critical properties are governed by the so-called Wilson-Fisher O(n) fixed point.

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“…[48], for Ho [49][50][51][52][53][54][55][56], for Dy [57][58][59][60][61][62][63] and for Tb [64][65][66][67][68]) could also be analyzed by the STA-model. For helimagnets the critical behavior is quite varied (see the review for Ho and Dy ref.…”

Section: Introductionmentioning

confidence: 99%

“…[54]). Essentially three types of results exist: one in favor of a O(4) class [54,55,61,62], another in favor of a new universality class [51,53,59,60,[64][65][66][67][68], and a third class which favor first order transition [50,57,58]. See Tables II-IV for details. With these results a definite answer cannot be given about the order of transition.…”

Section: Introductionmentioning

confidence: 99%

First and second order transition in frustrated XY systems

Loison

Schotte

1998

Eur. Phys. J. B

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The nature of the phase transition for the XY stacked triangular antiferromagnet (STA) is a controversial subject at present. The field theoretical renormalization group (RG) in three dimensions predicts a first order transition. This prediction disagrees with Monte Carlo (MC) simulations which favor a new universality class or a tricritical transition. We simulate by the Monte Carlo method two models derived from the STA by imposing the constraint of local rigidity which should have the same critical behavior as the original model. A strong first order transition is found. Following Zumbach we analyze the second order transition observed in MC studies as due to a fixed point in the complex plane. We review the experimental results in order to clarify the different critical behavior observed. P.A.C.S. numbers:05.70. Fh, 64.60.Cn,

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Thermal expansion in the magnetically ordered phases of holmium

Cited by 61 publications

References 11 publications

Nonperturbative renormalization-group approach to frustrated magnets

Nonperturbative renormalization-group approach to frustrated magnets

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First and second order transition in frustrated XY systems

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