Large-n expansion for m-axial Lifshitz points

The large-n expansion is developed for the study of critical behaviour of d-dimensional systems at m-axial Lifshitz points with an arbitrary number m of modulation axes. The leading non-trivial contributions of O(1/n) are derived for the two independent correlation exponents \eta_{L2} and \eta_{L4}, and the related anisotropy index \theta. The series coefficients of these 1/n corrections are given for general values of m and d with 0<m<d and 2+m/2<d<4+m/2 in the form of integrals. For special values of m and d such as (m,d)=(1,4), they can be computed analytically, but in general their evaluation requires numerical means. The 1/n corrections are shown to reduce in the appropriate limits to those of known large-n expansions for the case of d-dimensional isotropic Lifshitz points and critical points, respectively, and to be in conformity with available dimensionality expansions about the upper and lower critical dimensions. Numerical results for the 1/n coefficients of \eta_{L2}, \eta_{L4} and \theta are presented for the physically interesting case of a uniaxial Lifshitz point in three dimensions, as well as for some other choices of m and d. A universal coefficient associated with the energy-density pair correlation function is calculated to leading order in 1/n for general values of m and d.Comment: 28 pages, 3 figures. Submitted to: J. Phys. C: Solid State Phys., special issue dedicated to Lothar Schaefer on the occasion of his 60th birthday. V2: References added along with corresponding modifications in the text, corrected figure 3, corrected typo

Bulk and Boundary Critical Behavior at Lifshitz Points

Lifshitz points are multicritical points at which a disordered phase, a homogeneous ordered phase, and a modulated ordered phase meet. Their bulk universality classes are described by natural generalizations of the standard $\phi^4$ model. Analyzing these models systematically via modern field-theoretic renormalization group methods has been a long-standing challenge ever since their introduction in the middle of the 1970s. We survey the recent progress made in this direction, discussing results obtained via dimensionality expansions, how they compare with Monte Carlo results, and open problems. These advances opened the way towards systematic studies of boundary critical behavior at $m$-axial Lifshitz points. The possible boundary critical behavior depends on whether the surface plane is perpendicular to one of the $m$ modulation axes or parallel to all of them. We show that the semi-infinite field theories representing the corresponding surface universality classes in these two cases of perpendicular and parallel surface orientation differ crucially in their Hamiltonian's boundary terms and the implied boundary conditions, and explain recent results along with our current understanding of this matter.Comment: Invited contribution to STATPHYS 22, to be published in the Proceedings of the 22nd International Conference on Statistical Physics (STATPHYS 22) of the International Union of Pure and Applied Physics (IUPAP), 4--9 July 2004, Bangalore, Indi

Investibility and return volatility

Unlike previous studies that examine how emerging market return volatility changes subsequent to stock market liberalization, this paper investigates the impact of investibility, or the degree to which a stock can be foreign-owned, on emerging market volatility. We find a positive relation between return volatility and the investibility of individual stocks, even after controlling for country, industry, firm size, and turnover. We also find that a highly investible emerging market portfolio is subject to larger world market exposure than a non-investible portfolio, suggesting that highly investible stocks are more integrated with the world and therefore more vulnerable to world market risk. (C) 2003 Elsevier B.V. All rights reserved

Overnight information and intraday trading behavior: evidence from NYSE cross-listed stocks and their local market information

Abstract In this paper we study how overnight price movements in local markets affect the trading activity of foreign stocks on the NYSE. We find that local price movements affect not only the opening returns of foreign stocks, but also their returns in the first 30-min interval. The magnitude of local price movements is positively related to price volatility of foreign stocks, and this relation is stronger at the NYSE open and weaker afterward. This result helps explain why intraday price volatility is high at the open and lower at midday. However, local price movements cannot account for intraday variations in trading volume. We also find that trading volume for foreign stocks is strongly correlated with NYSE opening price volatility and weakly correlated with local market overnight price volatility. We interpret the result as evidence that the trading activity of foreign stocks on the NYSE is related more to liquidity trading of US investors and less to local market information