Susceptibility Amplitude Ratios Near a Lifshitz Point

The susceptibility amplitude ratio in the neighborhood of a uniaxial Lifshitz point is calculated at one-loop level using field-theoretic and $\epsilon_{L}$-expansion methods. We use the Schwinger parametrization of the propagator in order to split the quadratic and quartic part of the momenta, as well as a new special symmetry point suitable for renormalization purposes. For a cubic lattice (d = 3), we find the result $\frac{C_{+}}{C_{-}} = 3.85$.Comment: 7 pages, late

Reply to "Comment on Renormalization group picture of the Lifshitz critical behaviors"

We reply to a recent comment by Diehl and Shpot (cond-mat/0305131) criticizing a new approach to the Lifshitz critical behavior just presented (M. M. Leite Phys. Rev. B 67, 104415(2003)). We show that this approach is free of inconsistencies in the ultraviolet regime. We recall that the orthogonal approximation employed to solve arbitrary loop diagrams worked out at the criticized paper even at three-loop level is consistent with homogeneity for arbitrary loop momenta. We show that the criticism is incorrect.Comment: RevTex, 6 page

The antiferromagnetic phi4 Model, II. The one-loop renormalization

It is shown that the four dimensional antiferromagnetic lattice phi4 model has the usual non-asymptotically free scaling law in the UV regime around the chiral symmetrical critical point. The theory describes a scalar and a pseudoscalar particle. A continuum effective theory is derived for low energies. A possibility of constructing a model with a single chiral boson is mentioned.Comment: To appear in Phys. Rev.

Surface states in nearly modulated systems

A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model incorporates surface and bulk fields and includes a term in the free energy proportional to the square of the second derivative of the order parameter in addition to the usual term involving the square of the first derivative. In the limit of vanishing bulk field, three distinct types of surface ordering are possible: a wetting layer, a non-wet layer having a small deviation from bulk order, and a different non-wet layer with a large deviation from bulk order which decays non-monotonically as distance from the wall increases. In particular the large deviation non-wet layer is a feature of systems at the Lifshitz point and also those having only homogeneous bulk phases.Comment: 6 pages, 7 figures, submitted to Phys. Rev.

Revised Phase Diagram of the Gross-Neveu Model

We confirm earlier hints that the conventional phase diagram of the discrete chiral Gross-Neveu model in the large N limit is deficient at non-zero chemical potential. We present the corrected phase diagram constructed in mean field theory. It has three different phases, including a kink-antikink crystal phase. All transitions are second order. The driving mechanism for the new structure of baryonic matter in the Gross-Neveu model is an Overhauser type instability with gap formation at the Fermi surface.Comment: Revtex, 12 pages, 15 figures; v2: Axis labelling in Fig. 9 correcte

Thermodynamics of the incommensurate state in Rb_2WO_4: on the Lifshitz point in A`A``BX_4 compounds

We consider the evolution of the phase transition from the parent hexagonal phase $P6_{3}/mmc$ to the orthorhombic phase $Pmcn$ that occurs in several compounds of $A'A''BX_{4}$ family as a function of the hcp lattice parameter $c/a$. For compounds of $K_{2}SO_{4}$ type with $c/a$ larger than the threshold value 1.26 the direct first-order transition $Pmcn-P6_{3}/mmc$ is characterized by the large entropy jump $Rln2$. For compounds $Rb_{2}WO_{4}$, $K_{2}MoO_{4}$, $K_{2}WO_{4}$ with $c/a<1.26$ this transition occurs via an intermediate incommensurate $(Inc)$ phase. DSC measurements were performed in $Rb_{2}WO_{4}$ to characterize the thermodynamics of the $Pmcn-Inc-P6_{3}/mmc$ transitions. It was found that both transitions are again of the first order with entropy jumps $0.2Rln2 and$0.3Rln2$. Therefore, at$c/a ~ 1.26$the$A'A''BX_{4}$compounds reveal an unusual Lifshitz point where three first order transition lines meet. We propose the coupling of crystal elasticity with$BX_{4}$ tetrahedra orientation as a possible source of the transitions discontinuity.Comment: 13 pages,1 Postscript figure. Submitted as Brief Report to Phys. Rev. B, this paper reports a new work in Theory and Experiment, directed to Structural Phase Transition

Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes

The critical behavior of semi-infinite $d$-dimensional systems with $n$-component order parameter $\bm{\phi}$ and short-range interactions is investigated at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. The associated $m$ modulation axes are presumed to be parallel to the surface, where $0\le m\le d-1$. An appropriate semi-infinite $|\bm{\phi}|^4$ model representing the corresponding universality classes of surface critical behavior is introduced. It is shown that the usual O(n) symmetric boundary term $\propto \bm{\phi}^2$ of the Hamiltonian must be supplemented by one of the form $\mathring{\lambda} \sum_{\alpha=1}^m(\partial\bm{\phi}/\partial x_\alpha)^2$ involving a dimensionless (renormalized) coupling constant $\lambda$. The implied boundary conditions are given, and the general form of the field-theoretic renormalization of the model below the upper critical dimension $d^*(m)=4+{m}/{2}$ is clarified. Fixed points describing the ordinary, special, and extraordinary transitions are identified and shown to be located at a nontrivial value $\lambda^*$ if $\epsilon\equiv d^*(m)-d>0$. The surface critical exponents of the ordinary transition are determined to second order in $\epsilon$. Extrapolations of these $\epsilon$ expansions yield values of these exponents for $d=3$ in good agreement with recent Monte Carlo results for the case of a uniaxial ($m=1$) Lifshitz point. The scaling dimension of the surface energy density is shown to be given exactly by $d+m (\theta-1)$, where $\theta=\nu_{l4}/\nu_{l2}$ is the anisotropy exponent.Comment: revtex4, 31 pages with eps-files for figures, uses texdraw to generate some graphs; to appear in PRB; v2: some references and additional remarks added, labeling in figure 1 and some typos correcte

Fluctuations and Instabilities of Ferromagnetic Domain Wall pairs in an External Magnetic Field

Soliton excitations and their stability in anisotropic quasi-1D ferromagnets are analyzed analytically. In the presence of an external magnetic field, the lowest lying topological excitations are shown to be either soliton-soliton or soliton-antisoliton pairs. In ferromagnetic samples of macro- or mesoscopic size, these configurations correspond to twisted or untwisted pairs of Bloch walls. It is shown that the fluctuations around these configurations are governed by the same set of operators. The soliton-antisoliton pair has exactly one unstable mode and thus represents a critical nucleus for thermally activated magnetization reversal in effectively one-dimensional systems. The soliton-soliton pair is stable for small external fields but becomes unstable for large magnetic fields. From the detailed expression of this instability threshold and an analysis of nonlocal demagnetizing effects it is shown that the relative chirality of domain walls can be detected experimentally in thin ferromagnetic films. The static properties of the present model are equivalent to those of a nonlinear sigma-model with anisotropies. In the limit of large hard-axis anisotropy the model reduces to a double sine-Gordon model.Comment: 15 pages RevTex 3.0 (twocolumn), 9 figures available on request, to appear in Phys Rev B, Dec (1994

Universal finite-size scaling analysis of Ising models with long-range interactions at the upper critical dimensionality: Isotropic case

We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic whereby in the present work we focus on the isotropic case for which the model is found to be at its upper critical dimensionality. To investigate the critical behavior the temperature and field dependence of several quantities are studied by means of Monte Carlo simulations. On the basis of the Privman-Fisher hypothesis and results of the renormalization group the numerical data are analyzed in the framework of a finite-size scaling analysis and compared to finite-size scaling functions derived from a Ginzburg-Landau-Wilson model in zero mode (mean-field) approximation. The obtained excellent agreement suggests that at least in the present case the concept of universal finite-size scaling functions can be extended to the upper critical dimensionality.Comment: revtex4, 10 pages, 5 figures, 1 tabl

Anomalous dimensions and phase transitions in superconductors

The anomalous scaling in the Ginzburg-Landau model for the superconducting phase transition is studied. It is argued that the negative sign of the $\eta$ exponent is a consequence of a special singular behavior in momentum space. The negative sign of $\eta$ comes from the divergence of the critical correlation function at finite distances. This behavior implies the existence of a Lifshitz point in the phase diagram. The anomalous scaling of the vector potential is also discussed. It is shown that the anomalous dimension of the vector potential $\eta_A=4-d$ has important consequences for the critical dynamics in superconductors. The frequency-dependent conductivity is shown to obey the scaling $\sigma(\omega)\sim\xi^{z-2}$. The prediction $z\approx 3.7$ is obtained from existing Monte Carlo data.Comment: RevTex, 20 pages, no figures; small changes; version accepted in PR