Frustrated magnets in three dimensions: a nonperturbative approach

Frustrated magnets exhibit unusual critical behaviors: they display scaling laws accompanied by nonuniversal critical exponents. This suggests that these systems generically undergo very weak first order phase transitions. Moreover, the different perturbative approaches used to investigate them are in conflict and fail to correctly reproduce their behavior. Using a nonperturbative approach we explain the mismatch between the different perturbative approaches and account for the nonuniversal scaling observed.Comment: 7 pages, 1 figure. IOP style files included. To appear in Journal of Physics: Condensed Matter. Proceedings of the conference HFM 2003, Grenoble, Franc

Competition between fluctuations and disorder in frustrated magnets

We investigate the effects of impurities on the nature of the phase transition in frustrated magnets, in d=4-epsilon dimensions. For sufficiently small values of the number of spin components, we find no physically relevant stable fixed point in the deep perturbative region (epsilon << 1), contrarily to what is to be expected on very general grounds. This signals the onset of important physical effects.Comment: 4 pages, 3 figures, published versio

Optimization of the derivative expansion in the nonperturbative renormalization group

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the Principle of Minimal Sensitivity can be unambiguously implemented at order $\partial^2$ of the derivative expansion. This approach allows us to select optimized cut-off functions and to improve the accuracy of the critical exponents $\nu$ and $\eta$. The convergence of the field expansion is also analyzed. We show in particular that its optimization does not coincide with optimization of the accuracy of the critical exponents.Comment: 13 pages, 9 PS figures, published versio

Spin-stiffness and topological defects in two-dimensional frustrated spin systems

Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large class of Heisenberg frustrated spin systems. They are constructed so that to differ only by their topological properties. The spin-stiffnesses for the two systems of tops are calculated for different temperatures and different sizes of the sample. This allows to investigate the role of topological defects in frustrated spin systems. Comparisons with Renormalization Group results based on a Non Linear Sigma model approach and with the predictions of some simple phenomenological model taking into account the topological excitations are done.Comment: RevTex, 25 pages, 14 figures, Minor changes, final version. To appear in Phys.Rev.

Critical thermodynamics of three-dimensional chiral model for N > 3

The critical behavior of the three-dimensional $N$-vector chiral model is studied for arbitrary $N$. The known six-loop renormalization-group (RG) expansions are resummed using the Borel transformation combined with the conformal mapping and Pad\'e approximant techniques. Analyzing the fixed point location and the structure of RG flows, it is found that two marginal values of $N$ exist which separate domains of continuous chiral phase transitions $N > N_{c1}$ and $N N > N_{c2}$ where such transitions are first-order. Our calculations yield $N_{c1} = 6.4(4)$ and $N_{c2} = 5.7(3)$. For $N > N_{c1}$ the structure of RG flows is identical to that given by the $\epsilon$ and 1/N expansions with the chiral fixed point being a stable node. For $N < N_{c2}$ the chiral fixed point turns out to be a focus having no generic relation to the stable fixed point seen at small $\epsilon$ and large $N$. In this domain, containing the physical values $N = 2$ and $N = 3$, phase trajectories approach the fixed point in a spiral-like manner giving rise to unusual crossover regimes which may imitate varying (scattered) critical exponents seen in numerous physical and computer experiments.Comment: 12 pages, 3 figure

Fixed points in frustrated magnets revisited

We analyze the validity of perturbative renormalization group estimates obtained within the fixed dimension approach of frustrated magnets. We reconsider the resummed five-loop beta-functions obtained within the minimal subtraction scheme without epsilon-expansion for both frustrated magnets and the well-controlled ferromagnetic systems with a cubic anisotropy. Analyzing the convergence properties of the critical exponents in these two cases we find that the fixed point supposed to control the second order phase transition of frustrated magnets is very likely an unphysical one. This is supported by its non-Gaussian character at the upper critical dimension d=4. Our work confirms the weak first order nature of the phase transition occuring at three dimensions and provides elements towards a unified picture of all existing theoretical approaches to frustrated magnets.Comment: 18 pages, 8 figures. This article is an extended version of arXiv:cond-mat/060928

Partial loss of function of the GHRH Receptor leads to mild Growth Hormone Deficiency

OBJECTIVE: Recessive mutations in GHRHR are associated with severe isolated growth hormone deficiency (IGHD), with a final height in untreated patients of 130 cm ± 10 cm (-7.2 ± 1.6 SDS; males) and 114 ± 0.7 cm (-8.3 ± 0.1 SDS; females). DESIGN: We hypothesized that a consanguineous Pakistani family with IGHD in three siblings (two males, one female) would have mutations in GH1 or GHRHR. RESULTS: Two novel homozygous missense variants [c.11G>A (p.R4Q), c.236C>T (p.P79L)] at conserved residues were identified in all three siblings. Both were absent from control databases, aside from pR4Q appearing once in heterozygous form in the Exome Aggregation Consortium Browser. The brothers were diagnosed with GH deficiency at 9.8 and 6.0 years (height SDS: -2.24 and -1.23, respectively), with a peak GH of 2.9 μg/liter with low IGF-1/IGF binding protein 3. Their sister presented at 16 years with classic GH deficiency (peak GH <0.1 μg/liter, IGF-1 <3.3 mmol/liter) and attained an untreated near-adult height of 144 cm (-3.0 SDS); the tallest untreated patient with GHRHR mutations reported. An unrelated Pakistani female IGHD patient was also compound homozygous. All patients had a small anterior pituitary on magnetic resonance imaging. Functional analysis revealed a 50% reduction in maximal cAMP response to stimulation with GHRH by the p.R4Q/p.P79L double mutant receptor, with a 100-fold increase in EC50. CONCLUSION: We report the first coexistence of two novel compound homozygous GHRHR variants in two unrelated pedigrees associated with a partial loss of function. Surprisingly, the patients have a relatively mild IGHD phenotype. Analysis revealed that the pP79L mutation is associated with the compromise in function, with the residual partial activity explaining the mild phenotype

Spin Stiffness of Stacked Triangular Antiferromagnets

We study the spin stiffness of stacked triangular antiferromagnets using both heat bath and broad histogram Monte Carlo methods. Our results are consistent with a continuous transition belonging to the chiral universality class first proposed by Kawamura.Comment: 5 pages, 7 figure

Critical behavior of frustrated systems: Monte Carlo simulations versus Renormalization Group

We study the critical behavior of frustrated systems by means of Pade-Borel resummed three-loop renormalization-group expansions and numerical Monte Carlo simulations. Amazingly, for six-component spins where the transition is second order, both approaches disagree. This unusual situation is analyzed both from the point of view of the convergence of the resummed series and from the possible relevance of non perturbative effects.Comment: RevTex, 10 pages, 3 Postscript figure

A non perturbative approach of the principal chiral model between two and four dimensions

We investigate the principal chiral model between two and four dimensions by means of a non perturbative Wilson-like renormalization group equation. We are thus able to follow the evolution of the effective coupling constants within this whole range of dimensions without having recourse to any kind of small parameter expansion. This allows us to identify its three dimensional critical physics and to solve the long-standing discrepancy between the different perturbative approaches that characterizes the class of models to which the principal chiral model belongs.Comment: 5 pages, 1 figure, Revte