Field theoretical approach to gravitational waves

The aim of these notes is to give an accessible and self‐contained introduction to the theory of gravitational waves as the theory of a relativistic symmetric tensor field in a Minkowski background spacetime. This is the approach of a particle physicist: the graviton is identified with a particular irreducible representation of the Poincaré group, corresponding to vanishing mass and spin two. It is shown how to construct an action functional giving the linear dynamics of gravitons, and how General Relativity can be obtained from it. The Hamiltonian formulation of the linear theory is examined in detail. We study the emission of gravitational waves and apply the results to the simplest case of a binary Newtonian system.     

Field theories and growth models

Continuum field theories for the Eden and DLA models are formulated, and they are shown to be related to the reggeon field theories with local and non-local interactions, respectively.     

Dark Energy Cosmology with a Rarita-Schwinger Field

Recent observations of the Cosmic Microwave Background, Supernovae and Sloan Digital Sky Survey (SDSS) show that our universe has a critical energy density, and roughly 2/3 of it is dark energy, which drives the accelerating expansion of the cosmos. In view of the astrophysical data, we find that the equation of state parameter of the dark energy lies in a narrow range around w = −1. In this paper, we construct a cosmology model with a Rarita-Schwinger field to realize the equation of state parameter w < −1 or w > −1 and discuss its stability.     

A new approach to nonrenormalizable models

Nonrenormalizable quantum field theories require counter-terms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counter-terms suggested by renormalized perturbation theory are in fact inappropriate for this purpose. Guided by the potential underlying causes of triviality of such models, as obtained by alternative analyses, we focus attention on the ground-state distribution function, and suggest a formulation of such distributions that exhibits nontriviality from the start. Primary discussion is focused on self-interacting scalar fields. Conditions for bounds on general correlation functions are derived, and there is some discussion of the issues involved with the continuum limit.     

An Improved Heterogeneous Mean-Field Theory for the Ising Model on Complex Networks

Heterogeneous mean-field theory is commonly used methodology to study dynamical processes on complex networks,such as epidemic spreading and phase transitions in spin models.In this paper,we propose an improved heterogeneous mean-field theory for studying the Ising model on complex networks.Our method shows a more accurate prediction in the critical temperature of the Ising model than the previous heterogeneous mean-field theory.The theoretical results are validated by extensive Monte Carlo simulations in various types of networks.     

Virtual-site correlation mean field approach to criticality in spin systems

We propose a virtual-site correlation mean field theory for dealing with interacting many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory deals with only single-body physical parameters, the virtual-site correlation mean field theory deals with single- as well as two-body ones, and involves a virtual site for every interaction term in the Hamiltonian. We generalize the theory to a cluster virtual-site correlation mean field, that works with a fundamental unit of the lattice of the many-body system. We apply these methods to interacting Ising spin systems in several lattice geometries and dimensions, and show that the predictions of the onset of criticality of these models are generally much better in the proposed theories as compared to the corresponding ones in mean field theories.     

Metastability and exponential approach to equilibrium for low-temperature stochastic Ising models

We present a proof of the exponential convergence to equilibrium of single-spin-flip stochastic dynamics for the two-dimensional Ising ferromagnet in the low-temperature case with not too small external magnetic fieldh uniformly in the volume and in the boundary conditions.     

Mean-field bounds on the magnetization for ferromagnetic spin models

The mean-field approximation is shown to give an upper bound on the magnetization for a large class of one-component models with arbitrary ferromagnetic pair interactions. Specific examples include discrete and continuous spin Ising models. In addition, a new comparison inequality for multicomponent rotators is proven which allows this result to be extended to the plane rotator and classical Heisenberg ferromagnets.     

A set of exactly solvable Ising models with half-odd-integer spin

We present a set of exactly solvable Ising models, with half-odd-integer spin-S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin-(S,1/2) and only nearest-neighbor interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin-S lattice. By imposing the condition that the mixed half-odd-integer spin-(S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the free fermion condition of the eight vertex model. The number of solutions for a general half-odd-integer spin-S is given by S+1/2. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number.     

A theoretical study of magnetic phase transitions in ultra-thin films: Application to NiO

Phase diagrams and critical temperatures of projected onto fcc (1 0 0) layers, which is believed to be applicable to first-row transition metal oxides such as VO, MnO and NiO, are obtained from mean field theory and Monte Carlo simulations. Within the regime, J_se > 0, which includes MnO and NiO, both approaches predict bicritical behaviour of the AF₂ and AF₃ antiferromagnetic spin alignments for odd numbers of layers greater than one and monocritical behaviour for even numbers of layers, even when films are described by single values of J_d and J_se. The ferromagnetic alignment, on the other hand, exhibits monocritical behaviour for all thicknesses from the monolayer through to the bulk. For values of (x = J_d/J_se) which are close to those obtained from first principles calculations for NiO and also those derived from measured magnon spectra, estimates of the thickness dependence of the critical temperature from Monte Carlo simulations are similar to that derived from linear polarised X-ray absorption spectra of NiO(1 0 0) ultra-thin films grown epitaxially on MgO(1 0 0) [D. Alders, L.H. Tjeng, F.C. Voogt, T. Hibma, G.A. Sawatzky, J. Vogel, M. Sacchi, S. Iacobucci, Phys. Rev. B 57 (1998) 11623].     

Thermodynamical Properties of Spin-3/2 Ising Model in a Longitudinal Random Field with Crystal Field

A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studiedby using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point areinvestigated numerically for the honeycomb lattice when the randorm field is bimodal. In particular, the specific heatand the internal energy are examined in detail for the system with a crystal-field constant in the critical region wherethe ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interestingphenomena in the system.     

动力学伊辛模型在振荡外场中的成核

研究了二维的动力学伊辛模型在一个具有偏向的振荡外场中的成核过程,主要关注成核时间与外场振荡周期ω的关系．随着ω的变化,成核时间出现最小值,最小的成核时间对应的平均临界核的大小也是最小的,这表明存在一个最佳的振荡频率,相比较于一个确定的外场,它更有利于成核．同时还研究了外场的初始相位的影响．     

Thermodynamical Properties of Spin-3/2 Ising Model in a Longitudinal Random Field with Crystal Field

A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studied by using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point are investigated numerically for the honeycomb lattice when the random field is bimodal. In particular, the specific heat and the internal energy are examined in detail for the system with a crystal-field constant in the critical region where the ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interesting phenomena in the system.     

Absence of tricritical behavior of the random field Ising model in a honyecomb lattice

In this letter, we study the behavior of the random field Ising model on a honeycomb lattice by means of the effective field theory. We obtain the phase diagram in the T$T$–H$H$ plane for clusters with one spin in a finite size cluster scheme and it is observed the absence of a tricritical point.     

Combinatorial Dyson–Schwinger equations and inductive data type

The goal of this contribution is to explain the analogy between combinatorial Dyson–Schwinger equations and inductive data types to a readership of mathematical physicists. The connection relies on an interpretation of combinatorial Dyson–Schwinger equations as fixpoint equations for olynomial functors (established elsewhere by the author, and summarised here), combined with he now-classical fact that polynomial functors provide semantics for inductive types. The paper is xpository, and comprises also a brief introduction to type theory.     

A brief review of continuous models for ionic solutions: the Poisson-Boltzmann and related theories

The Poisson–Boltzmann (PB) theory is one of the most important theoretical models describing charged systems continuously. However, it suffers from neglecting ion correlations, which hinders its applicability to more general charged systems other than extremely dilute ones. Therefore, some modified versions of the PB theory are developed to effectively include ion correlations. Focused on their applications to ionic solutions, the original PB theory and its variances, including the field-theoretic approach, the correlation-enhanced PB model, the Outhwaite–Bhuiyan modified PB theory and the mean field theories, are briefly reviewed in this paper with the diagnosis of their advantages and limitations.     

A measure of statistical complexity based on predictive information with application to finite spin systems

We propose the binding information as an information theoretic measure of complexity between multiple random variables, such as those found in the Ising or Potts models of interacting spins, and compare it with several previously proposed measures of statistical complexity, including excess entropy, Bialek et al.?s predictive information, and the multi-information. We discuss and prove some of the properties of binding information, particularly in relation to multi-information and entropy, and show that, in the case of binary random variables, the processes which maximise binding information are the ‘parity’ processes. The computation of binding information is demonstrated on Ising models of finite spin systems, showing that various upper and lower bounds are respected and also that there is a strong relationship between the introduction of high-order interactions and an increase of binding-information. Finally we discuss some of the implications this has for the use of the binding information as a measure of complexity.