Translation-invariant Model Research Articles

Critical Behavior in a Quasi D Dimensional Spin Model

We study a classical spin model (more precisely a class of models) with O(N) symmetry that can be viewed as a simplified D dimensional lattice model. It is equivalent to a non-translationinvariant one dimensional model and contains the dimensionality D as a parameter that need not be an integer. The critical dimension turns out to be 2, just as in the usual translation invariant models. We study the phase structure, critical phenomena and spontaneous symmetry breaking. Furthermore we compute the perturbation expansion to low order with various boundary conditions. In our simplified models a number of questions can be answered that remain controversial in the translation invariant models, such as the asymptoticity of the perturbation expansion and the role of super-instantons. We find that perturbation theory produces the right asymptotic expansion in dimension D≤2 only with special boundary conditions. Finally the model allows a test of the percolation ideas of Patrascioiu and Seiler.

SHELL MODEL CALCULATIONS OF 3T, 5He AND 6Li NUCLEI

The bases of the translation invariant shell model are used to construct the ground-state wave functions of 3 T , 5 He and 6 Li . For 3 T the bases used correspond to the number of quanta of excitation N up to ten. For 5 He and 6 Li the bases used correspond to the number of quanta of excitation N up to six. The model is applied to calculate the binding energy and the root mean square radius for 3 T , 5 He and 6 Li nuclei. The residual interactions used consist of central, tensor, spin-orbit and quadratic spin-orbit terms with Gaussian radial dependence. The parameters of these interactions are chosen in such away that they represent the long range attraction and the short range repulsion of nucleon interactions. It was found that this potential is more suitable for calculating the characteristics of these nuclei, and better than other potentials, such as our previous potentials which were represented by the parameters of long range attraction forces only. For 3T we obtained good agreement between calculated and experimental values of both the ground state binding energy and the root mean square radius. For 5 He and 6 Li nuclei we obtained an acceptable improvement with these calculations over other potentials.

Suppression of Critical Fluctuations by Strong Quantum Effects in Quantum Lattice System

Translation invariant models of quantum anharmonic oscillators with a polynomial anharmonicity and a ferroelectric interaction are considered. For these models, it is proved that the critical fluctuations of the position operator, peculiar to the critical point, are suppressed at all temperatures provided the oscillators are strongly quantum. This phenomenon is shown to occur in particular if the oscillator's mass is less than some threshold value depending on the anharmonicity parameters.

Units invariant and translation invariant DEA models

In this paper we discuss the desirable properties of units invariance and translation invariance, and we note which DEA models satisfy one or the other of these properties. No currently known DEA model satisfies both properties. We then introduce two new DEA models. One satisfies units invariance and partial translation invariance, and the other satisfies both properties.

Solvable (nonrelativistic, classical) n-body problems on the line. I

Several solvable n-body problems on the line are exhibited. They are characterized by equations of motion of Newtonian type, mjẍj=Fj, j=1,...,n, with the ‘‘forces’’ Fj given as explicit functions of the ‘‘particle coordinates’’ xk and their velocities ẋk, k=1,...,n; the forces Fj generally also depend on some free parameters, so that in each case there is actually a class of solvable models. In this paper the emphasis is on translation-invariant models, and on values of n sufficiently small (‘‘few-body problems’’) to allow the display of the solution of the initial-value problem in completely explicit form.

Robust Bayesian Credible Intervals and Prior Ignorance

Summary In this paper we propose, survey and compare some classes of probability densities that may be used to represent partial prior information, to model either prior ignorance or Bayesian sensitivity analysis. We distinguish two types of models appropriate for two different situations: near ignorance models which are suitable in problems where there is little prior information, and neighbourhood models, which can be used to 'robustify' a strict Bayesian analysis in problems where there is substantial prior information about location. We argue that, especially for the first situation, a reasonable class of prior densities is not the same as a class of reasonable prior densities. We discuss various desiderata for a 'reasonable' class, including coherence and sensible dependence of inferences on sample size. The translation invariant models studied here are classes of conjugate priors, classes of double exponential densities and a neighbourhood of the uniform prior. Of the neighbourhood models we examine examples of E-contamination neighbourhoods (previously studied by Huber, Berger and Berliner) and intervals of measures (DeRobertis and Hartigan). We illustrate the models in the simple problem of constructing credible intervals for an unknown normal mean. Of the models studied in detail, a translation-invariant class of double exponential priors is favoured for modelling little prior information, and a type of interval of measures seems most suitable for robust Bayesian analysis.

Effects of core motion on the nucleon electric form factors.

When the nucleon is described as the self-consistent nontopological soliton ground state of a translation-invariant model Hamiltonian for a nonstatic baglike core interacting with a pion field, the motion of the core is shown to have a significant effect on the proton and neutron electric form factors, as compared to previous cloudy-bag-model (CBM) calculations that neglect the core motion and treat the baglike core as a static source of pion field. In the translation-invariant model, the charge density of the nucleon has contributions from the core and from the pion cloud, as in the usual static CBM; in addition, and in contrast to the usual static CBM, there are effects due to the spreading of the core charge density as a result of the self-consistent motion of the core within the pion field that it generates. The spreading of the core density tends to weaken the core-pion interaction for a fixed bag radius so that the binding of the core-pion system is less than in the static cloudy bag. Hence, the motion of the core softens the electric form factors as compared to static CBM calculations.

Transfer tensor method applied to translation invariant models

Abstract The transfer tensor method is used to calculate partition functions and correlation functions for a large class of translation invariant models in d dimensions.