The critical behavior of frustrated spin models with noncollinear order

We study the critical behavior of frustrated spin models with noncollinear order, including stacked triangular antiferromagnets and helimagnets. For this purpose we compute the field-theoretic expansions at fixed dimension to six loops and determine their large-order behavior. For the physically relevant cases of two and three components, we show the existence of a new stable fixed point that corresponds to the conjectured chiral universality class. This contradicts previous three-loop field-theoretical results but is in agreement with experiments.Comment: 4 pages, RevTe

Pores in Bilayer Membranes of Amphiphilic Molecules: Coarse-Grained Molecular Dynamics Simulations Compared with Simple Mesoscopic Models

We investigate pores in fluid membranes by molecular dynamics simulations of an amphiphile-solvent mixture, using a molecular coarse-grained model. The amphiphilic membranes self-assemble into a lamellar stack of amphiphilic bilayers separated by solvent layers. We focus on the particular case of tension less membranes, in which pores spontaneously appear because of thermal fluctuations. Their spatial distribution is similar to that of a random set of repulsive hard discs. The size and shape distribution of individual pores can be described satisfactorily by a simple mesoscopic model, which accounts only for a pore independent core energy and a line tension penalty at the pore edges. In particular, the pores are not circular: their shapes are fractal and have the same characteristics as those of two dimensional ring polymers. Finally, we study the size-fluctuation dynamics of the pores, and compare the time evolution of their contour length to a random walk in a linear potential

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

Charge orderings in the atomic limit of the extended Hubbard model

The extended Hubbard model in the atomic limit (AL-EHM) on a square lattice with periodic boundary conditions is studied with use of the Monte Carlo (MC) method. Within the grand canonical ensemble the phase and order-order boundaries for charge orderings are obtained. The phase diagrams include three types of charge ordered phases and the nonordered phase. The system exhibits very rich structure and shows unusual multicritical behavior. In the limiting case of tij = 0, the EHM is equivalent to the pseudospin model with single-ion anisotropy 1/2U, exchange interaction W in an effective magnetic field (mu-1/2U-zW). This classical spin model is analyzed using the MC method for the canonical ensemble. The phase diagram is compared with the known results for the Blume-Capel model.Comment: 9 pages, 10 figure

Critical behavior of O(2)xO(N) symmetric models

We investigate the controversial issue of the existence of universality classes describing critical phenomena in three-dimensional statistical systems characterized by a matrix order parameter with symmetry O(2)xO(N) and symmetry-breaking pattern O(2)xO(N) -> O(2)xO(N-2). Physical realizations of these systems are, for example, frustrated spin models with noncollinear order. Starting from the field-theoretical Landau-Ginzburg-Wilson Hamiltonian, we consider the massless critical theory and the minimal-subtraction scheme without epsilon expansion. The three-dimensional analysis of the corresponding five-loop expansions shows the existence of a stable fixed point for N=2 and N=3, confirming recent field-theoretical results based on a six-loop expansion in the alternative zero-momentum renormalization scheme defined in the massive disordered phase. In addition, we report numerical Monte Carlo simulations of a class of three-dimensional O(2)xO(2)-symmetric lattice models. The results provide further support to the existence of the O(2)xO(2) universality class predicted by the field-theoretical analyses.Comment: 45 pages, 20 figs, some additions, Phys.Rev.B in pres

Testing for Features in the Primordial Power Spectrum

Well-known causality arguments show that events occurring during or at the end of inflation, associated with reheating or preheating, could contribute a blue component to the spectrum of primordial curvature perturbations, with the dependence k^3. We explore the possibility that they could be observably large in CMB, LSS, and Lyman-alpha data. We find that a k^3 component with a cutoff at some maximum k can modestly improve the fits (Delta chi^2=2.0, 5.4) of the low multipoles (l ~ 10 - 50) or the second peak (l ~ 540) of the CMB angular spectrum when the three-year WMAP data are used. Moreover, the results from WMAP are consistent with the CBI, ACBAR, 2dFGRS, and SDSS data when they are included in the analysis. Including the SDSS galaxy clustering power spectrum, we find weak positive evidence for the k^3 component at the level of Delta chi' = 2.4, with the caveat that the nonlinear evolution of the power spectrum may not be properly treated in the presence of the k^3 distortion. To investigate the high-k regime, we use the Lyman-alpha forest data (LUQAS, Croft et al., and SDSS Lyman-alpha); here we find evidence at the level Delta chi^2' = 3.8. Considering that there are two additional free parameters in the model, the above results do not give a strong evidence for features; however, they show that surprisingly large bumps are not ruled out. We give constraints on the ratio between the k^3 component and the nearly scale-invariant component, r_3 < 1.5, over the range of wave numbers 0.0023/Mpc < k < 8.2/Mpc. We also discuss theoretical models which could lead to the k^3 effect, including ordinary hybrid inflation and double D-term inflation models. We show that the well-motivated k^3 component is also a good representative of the generic spikelike feature in the primordial perturbation power spectrum.Comment: 23 pages, 6 figures; added new section on theoretical motivation for k^3 term, and discussion of double D-term hybrid inflation models; title changed, added a new section discussing the generic spikelike features, published in IJMP

Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ϕ4\phi^4 model

With the help of the improved Monte Carlo renormalization-group scheme, we numerically investigate the renormalization group flow of the antiferromagnetic Heisenberg and XY spin model on the stacked triangular lattice (STA-model) and its effective Hamiltonian, 2N-component chiral $\phi^4$ model which is used in the field-theoretical studies. We find that the XY-STA model with the lattice size $126\times 144 \times 126$ exhibits clear first-order behavior. We also find that the renormalization-group flow of STA model is well reproduced by the chiral $\phi^4$ model, and that there are no chiral fixed point of renormalization-group flow for N=2 and 3 cases. This result indicates that the Heisenberg-STA model also undergoes first-order transition.Comment: v1:15 pages, 15 figures v2:updated references v3:added comments on the higher order irrelevant scaling variables v4:added results of larger sizes v5:final version to appear in J.Phys.Soc.Jpn Vol.72, No.

Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering

The fixed point that governs the critical behavior of magnets described by the $N$-vector chiral model under the physical values of $N$ ($N =2, 3$) is shown to be a stable focus both in two and three dimensions. Robust evidence in favor of this conclusion is obtained within the five-loop and six-loop renormalization-group analysis in fixed dimension. The spiral-like approach of the chiral fixed point results in unusual crossover and near-critical regimes that may imitate varying critical exponents seen in physical and computer experiments.Comment: 4 pages, 5 figures. Discussion enlarge

Nonperturbative renormalization group approach to frustrated magnets

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. 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.Comment: 58 pages, 15 PS figure

Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice

We study the anti-ferromagnetic six-state clock model with nearest neighbor interactions on a triangular lattice with extensive Monte-Carlo simulations. We find clear indications of two phase transitions at two different temperatures: Below $T_I$ a chirality order sets in and by a thorough finite size scaling analysis of the specific heat and the chirality correlation length we show that this transition is in the Ising universality class (with a non-vanishing chirality order parameter below $T_I$). At $T_{KT}(<T_I)$ the spin-spin correlation length as well as the spin susceptibility diverges according to a Kosterlitz-Thouless (KT) form and spin correlations decay algebraically below $T_{KT}$. We compare our results to recent x-ray diffraction experiments on the orientational ordering of CF$_3$Br monolayers physisorbed on graphite. We argue that the six-state clock model describes the universal feature of the phase transition in the experimental system and that the orientational ordering belongs to the KT universality class.Comment: 8 pages, 9 figure