Magnetization reversal times in the 2D Ising model

We present a theoretical framework which is generally applicable to the study of time scales of activated processes in systems with Brownian type dynamics. This framework is applied to a prototype system: magnetization reversal times in the 2D Ising model. Direct simulation results for the magnetization reversal times, spanning more than five orders of magnitude, are compared with theoretical predictions; the two agree in most cases within 20%.Comment: 9 pages, 8 figure

Asymptotic Sign-Solvability, Multiple Objective Linear Programming, and The Nonsubstitution Theorem

In this paper we investigate the asymptotic stability of dynamic, multiple-objective linear programs. In particular, we show that a generalization of the optimal partition stabilizes for a large class of data functions. This result is based on a new theorem about asymptotic sign-solvable systems. The stability properties of the generalized optimal partition are used to extend a dynamic version of the Nonsubstitution Theorem

Monte Carlo Determination of Multiple Extremal Eigenpairs

We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector. The new algorithm, a Monte Carlo implementation of a deterministic one we recently benchmarked, is an extension of the power method. In the implementation presented, we used a basic Monte Carlo splitting and termination method called the comb, incorporated the weight cancellation method of Arnow {\it et al.}, and exploited a new sampling method, the sewing method, that does a large state space sampling as a succession of small state space samplings. We illustrate the effectiveness of the algorithm by its determination of the two largest eigenvalues of the transfer matrices for variously-sized two-dimensional, zero field Ising models. While very likely useful for other transfer matrix problems, the algorithm is however quite general and should find application to a larger variety of problems requiring a few dominant eigenvalues of a matrix.Comment: 22 pages, no figure

High precision Monte Carlo study of the 3D XY-universality class

We present a Monte Carlo study of the two-component $\phi^4$ model on the simple cubic lattice in three dimensions. By suitable tuning of the coupling constant $\lambda$ we eliminate leading order corrections to scaling. High statistics simulations using finite size scaling techniques yield $\nu=0.6723(3)[8]$ and $\eta=0.0381(2)[2]$, where the statistical and systematical errors are given in the first and second bracket, respectively. These results are more precise than any previous theoretical estimate of the critical exponents for the 3D XY universality class.Comment: 13 page

A Density Matrix Algorithm for 3D Classical Models

We generalize the corner transfer matrix renormalization group, which consists of White's density matrix algorithm and Baxter's method of the corner transfer matrix, to three dimensional (3D) classical models. The renormalization group transformation is obtained through the diagonalization of density matrices for a cubic cluster. A trial application for 3D Ising model with m=2 is shown as the simplest case.Comment: 15 pages, Latex(JPSJ style files are included), 8 ps figures, submitted to J. Phys. Soc. Jpn., some references are correcte

Numerical Study of a Mixed Ising Ferrimagnetic System

We present a study of a classical ferrimagnetic model on a square lattice in which the two interpenetrating square sublattices have spins one-half and one. This model is relevant for understanding bimetallic molecular ferrimagnets that are currently being synthesized by several experimental groups. We perform exact ground-state calculations for the model and employ Monte Carlo and numerical transfer-matrix techniques to obtain the finite-temperature phase diagram for both the transition and compensation temperatures. When only nearest-neighbor interactions are included, our nonperturbative results indicate no compensation point or tricritical point at finite temperature, which contradicts earlier results obtained with mean-field analysis.Comment: Figures can be obtained by request to [email protected] or [email protected]

An algorithm to calculate the transport exponent in strip geometries

An algorithm for solving the random resistor problem by means of the transfer-matrix approach is presented. Preconditioning by spanning clusters extraction both reduces the size of the conductivity matrix and speed up the calculations.Comment: 17 pages, RevTeX2.1, HLRZ - 97/9

Field-Induced Transition in the S=1 Antiferromagnetic Chain with Single-Ion Anisotropy in a Transverse Magnetic Field

The field-induced transition in one-dimensional S=1 Heisenberg antiferromagnet with single-ion anisotropy in the presence of a transverse magnetic field is obtained on the basis of the Schwinger boson mean-field theory. The behaviors of the specific heat and susceptibility as functions of temperature as well as the applied transverse field are explored, which are found to be different from the results obtained under a longitudinal field. The anomalies of the specific heat at low temperatures, which might be an indicative of a field-induced transition from a Luttinger liquid phase to an ordered phase, are explicitly uncovered under the transverse field. A schematic phase diagram is proposed. The theoretical results are compared with experimental observations.Comment: Revtex, 7 figure

Two-Dimensional Quantum Spin Systems with Ladder and Plaquette Structure

We investigate low-energy properties of two-dimensional quantum spin systems with the ladder and plaquette structures, which are described by a generalized antiferromagnetic Heisenberg model with both of the bond and spin alternations. By exploiting a non-linear $\sigma$ model technique and a modified spin wave approach, we evaluate the spin gap and the spontaneous magnetization to discuss the quantum phase transition between the ordered and disordered states. We argue how the spin-gapped phase is driven to the antiferromagnetic phase in the phase diagram.Comment: 8 pages (9 figures), accepted by JPS

Reassessing Ethnic Differences in Mean BMI and Changes Between 2007 and 2013 in English Children.

OBJECTIVE: National body fatness (BF) data for English South Asian and Black children use BMI, which provides inaccurate ethnic comparisons. BF levels and time trends in the English National Child Measurement Programme (NCMP) between 2007 and 2013 were assessed by using ethnic-specific adjusted BMI (aBMI) for South Asian and Black children. METHODS: Analyses were based on 3,195,323 children aged 4 to 5 years and 2,962,673 children aged 10 to 11 years. aBMI values for South Asian and Black children (relating to BF as in White children) were derived independently. Mean aBMI levels and 5-year aBMI changes were obtained by using linear regression. RESULTS: In the 2007-2008 NCMP, mean aBMIs in 10- to 11-year-old children (boys, girls) were higher in South Asian children (20.1, 19.9 kg/m2 ) and Black girls, but not in Black boys (18.4, 19.2 kg/m2 ) when compared with White children (18.6, 19.0 kg/m2 ; all P < 0.001). Mean 5-year changes (boys, girls) were higher in South Asian children (0.16, 0.32 kg/m2 per 5 y; both P < 0.001) and Black boys but not girls (0.13, 0.15 kg/m2 per 5 y; P = 0.01, P = 0.41) compared with White children (0.02, 0.11 kg/m2 per 5 y). Ethnic differences at 4 to 5 years were similar. Unadjusted BMI showed similar 5-year changes but different mean BMI patterns. CONCLUSIONS: BF levels were higher in South Asian children than in other groups in 2007 and diverged from those in White children until 2013, a pattern not apparent from unadjusted BMI data