Series Analysis of Tricritical Behavior: Mean-Field Model and Slicewise Pade Approximants

A mean-field model is proposed as a test case for tricritical series analyses methods. Derivation of the 50th order series for the magnetization is reported. As the first application this series is analyzed by the traditional slicewise Pade approximant method popular in earlier studies of tricriticality.Comment: 22 pages in plain TeX; 7 PostScript figs available by e-mai

The critical Ising lines of the d=2 Ashkin-Teller model

The universal critical point ratio $Q$ is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the ratio $Q$ in the presence of a non-vanishing thermal field is found from finite-size scaling and the corresponding expression is fitted to the accurate perturbative transfer-matrix data calculations for the $L\times L$ square clusters with $L\leq 9$.Comment: RevTex, 4 pages, two figure

Random Field Models for Relaxor Ferroelectric Behavior

Heat bath Monte Carlo simulations have been used to study a four-state clock model with a type of random field on simple cubic lattices. The model has the standard nonrandom two-spin exchange term with coupling energy $J$ and a random field which consists of adding an energy $D$ to one of the four spin states, chosen randomly at each site. This Ashkin-Teller-like model does not separate; the two random-field Ising model components are coupled. When $D / J = 3$, the ground states of the model remain fully aligned. When $D / J \ge 4$, a different type of ground state is found, in which the occupation of two of the four spin states is close to 50%, and the other two are nearly absent. This means that one of the Ising components is almost completely ordered, while the other one has only short-range correlations. A large peak in the structure factor $S (k)$ appears at small $k$ for temperatures well above the transition to long-range order, and the appearance of this peak is associated with slow, "glassy" dynamics. The phase transition into the state where one Ising component is long-range ordered appears to be first order, but the latent heat is very small.Comment: 7 pages + 12 eps figures, to appear in Phys Rev

Critical behaviour of the Random--Bond Ashkin--Teller Model, a Monte-Carlo study

The critical behaviour of a bond-disordered Ashkin-Teller model on a square lattice is investigated by intensive Monte-Carlo simulations. A duality transformation is used to locate a critical plane of the disordered model. This critical plane corresponds to the line of critical points of the pure model, along which critical exponents vary continuously. Along this line the scaling exponent corresponding to randomness $\phi=(\alpha/\nu)$ varies continuously and is positive so that randomness is relevant and different critical behaviour is expected for the disordered model. We use a cluster algorithm for the Monte Carlo simulations based on the Wolff embedding idea, and perform a finite size scaling study of several critical models, extrapolating between the critical bond-disordered Ising and bond-disordered four state Potts models. The critical behaviour of the disordered model is compared with the critical behaviour of an anisotropic Ashkin-Teller model which is used as a refference pure model. We find no essential change in the order parameters' critical exponents with respect to those of the pure model. The divergence of the specific heat $C$ is changed dramatically. Our results favor a logarithmic type divergence at $T_{c}$, $C\sim \log L$ for the random bond Ashkin-Teller and four state Potts models and $C\sim \log \log L$ for the random bond Ising model.Comment: RevTex, 14 figures in tar compressed form included, Submitted to Phys. Rev.

Dynamic Critical Behavior of a Swendsen-Wang-Type Algorithm for the Ashkin-Teller Model

We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin--Teller model. We find that the Li--Sokal bound on the autocorrelation time ($\tau_{{\rm int},{\cal E}} \ge {\rm const} \times C_H$) holds along the self-dual curve of the symmetric Ashkin--Teller model, and is almost but not quite sharp. The ratio $\tau_{{\rm int},{\cal E}} / C_H$ appears to tend to infinity either as a logarithm or as a small power ($0.05 \leq p \leq 0.12$). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.Comment: 59 pages including 3 figures, uuencoded g-compressed ps file. Postscript size = 799740 byte

Innate Immune Function in Placenta and Cord Blood of Hepatitis C – Seropositive Mother-Infant Dyads

Vertical transmission accounts for the majority of pediatric cases of hepatitis C viral (HCV) infection. In contrast to the adult population who develop persistent viremia in ∼80% of cases following exposure, the rate of mother-to-child transmission (2–6%) is strikingly low. Protection from vertical transmission likely requires the coordination of multiple components of the immune system. Placenta and decidua provide a direct connection between mother and infant. We hypothesized that innate immune responses would differ across the three compartments (decidua, placenta and cord blood) and that hepatitis C exposure would modify innate immunity in these tissues. The study was comprised of HCV-infected and healthy control mother and infant pairs from whom cord blood, placenta and decidua were collected with isolation of mononuclear cells. Multiparameter flow cytometry was performed to assess the phenotype, intracellular cytokine production and cytotoxicity of the cells. In keeping with a model where the maternal-fetal interface provides antiviral protection, we found a gradient in proportional frequencies of NKT and γδ-T cells being higher in placenta than cord blood. Cytotoxicity of NK and NKT cells was enhanced in placenta and placental NKT cytotoxicity was further increased by HCV infection. HCV exposure had multiple effects on innate cells including a decrease in activation markers (CD69, TRAIL and NKp44) on NK cells and a decrease in plasmacytoid dendritic cells in both placenta and cord blood of exposed infants. In summary, the placenta represents an active innate immunological organ that provides antiviral protection against HCV transmission in the majority of cases; the increased incidence in preterm labor previously described in HCV-seropositive mothers may be related to enhanced cytotoxicity of NKT cells