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We critically discuss the arguments reported in cond-mat/0609285 by B. Delamotte, Yu. Holovatch, D. Ivaneyko, D. Mouhanna, and M. Tissier. We show that their conclusions are not theoretically founded. They are contradicted by theoretical…
We analyze the validity of perturbative estimations obtained at fixed dimensions in the study of frustrated magnets. To this end we consider the five-loop beta-functions obtained within the minimal subtraction scheme and exploited without…
We show that the critical behaviour of two- and three-dimensional frustrated magnets cannot reliably be described from the known five- and six-loops perturbative renormalization group results. Our conclusions are based on a careful…
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…
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…
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…
Frustrated magnets are a notorious example where the usual perturbative methods are in conflict. Using a nonperturbative Wilson-like approach, we get a coherent picture of the physics of Heisenberg frustrated magnets everywhere between…
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…
XY frustrated magnets exhibit an unsual critical behavior: they display scaling laws accompanied by nonuniversal critical exponents and a negative anomalous dimension. This suggests that they undergo weak first order phase transitions. We…
Frustrated magnetism plays a central role in the phenomenology of exotic quantum states. However, because the magnetic structures of frustrated systems are aperiodic, there has always been the problem that they cannot be determined using…
Frustrated magnets are a notorious example where usual perturbative methods fail. Having recourse to an exact renormalization group approach, one gets a coherent picture of the physics of Heisenberg frustrated magnets everywhere between d=2…
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…
In these lectures we sketch a rapid survey of recent theoretical advances in the study of frustrated quantum magnets with a special emphasis on two dimensional magnets.
We present a brief overview on some of the most significant achievements obtained by means of NMR and muSR techniques in highly frustrated magnets. First the basic quantities measured by the two techniques will be presented and their…
For two spatially anisotropic, SU(2)-invariant models of frustrated magnets in arbitrary space dimension we present a non-perturbative proof of the existence of neutral spin-1/2 excitations (spinons). In one model the frustration is static…
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…
We present a unified approach to the problem of degeneracy lifting in geometrically frustrated magnets with and without an external field. The method treats fluctuations around a classical spin configuration in terms of a real-space…
Earlier work on dynamical critical phenomena in the context of magnetic hysteresis for uniaxial (scalar) spins, is extended to the case of a multicomponent (vector) field. From symmetry arguments and a perturbative renormalization group…
We study critical behaviour of a magnet with cubic anisotropy and quenched scalar disorder which is taken into account by replica method. We derive to first order in $\epsilon$ approximation the renormalization group equations taking into…
We argue that collinearly ordered states which exist in strongly frustrated spin systems for special rational values of the magnetization are stabilized by thermal as well as quantum fluctuations. These general predictions are tested by…