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## Full-Text Articles in Physics

Critical Behavior Of The One-Dimensional *S* = 1 *Xy* Model With Single-Ion Anisotropy, O. F. De Alcantara Bonfim, T. Schneider

#### Critical Behavior Of The One-Dimensional S = 1 Xy Model With Single-Ion Anisotropy, O. F. De Alcantara Bonfim, T. Schneider

*Physics Faculty Publications and Presentations*

We study the quantum critical behavior of the one-dimensional, *S *= 1 *XY* model in the presence of a single-ion anisotropy. Using a path-integral approach, we obtain, at *T* = 0 and for a positive anisotropy constant, a classical free-energy functional that allows discussion of the critical properties. The rescaling of frequencies is governed by the critical exponent *z* = 1. Renormalization-group arguments reveal that at criticality the system belongs to the same universality class as the isotropic 2-*d XY* model.

Energy Losses Of Solar Neutrinos And The Oscillation Hypothesis, P.T. Leung, S. Boedo, M. L. Rustgi

#### Energy Losses Of Solar Neutrinos And The Oscillation Hypothesis, P.T. Leung, S. Boedo, M. L. Rustgi

*Physics Faculty Publications and Presentations*

A formula for the stopping power of neutrinos interacting via the standard weak-interaction model, but incorporating the possibility of neutrino oscillations among the three flavors, is derived. The results are applied to study the solar-neutrino anomaly and it is found that the anomaly cannot be accounted for by many orders of magnitude from consideration of the energy losses of the neutrinos interacting with the solar matter, even if the oscillation hypothesis is found to be valid.

General Formula For The Inelastic Scattering Of Relativistic Spin-½ Particles By Heavy Atoms, P.T. Leung, M. L. Rustgi, S. A. Long

#### General Formula For The Inelastic Scattering Of Relativistic Spin-½ Particles By Heavy Atoms, P.T. Leung, M. L. Rustgi, S. A. Long

*Physics Faculty Publications and Presentations*

A general differential-cross-section formula for the inelastic scattering of relativistic spin-½ particles by heavy atoms is derived in the Born approximation and the structure and polarization of the incident particle is incorporated. The results reduce to those of Fano (1963) and of Turner et al. (1973) in well-known limiting cases.

Coexistence And Spinodal Curves In Directionally Bonded Liquids Using The Four-Cluster Approximation, Erik Bodegom, Paul H. Meijer

#### Coexistence And Spinodal Curves In Directionally Bonded Liquids Using The Four-Cluster Approximation, Erik Bodegom, Paul H. Meijer

*Physics Faculty Publications and Presentations*

We derive the phase diagrams and spinodals of binary liquid systems with anisotropic interactions, such as hydrogen-bonded molecules. The work is based on the four-particle cluster variation method, using a different potential for different contact points. It is shown that the introduction of a cluster larger than previously used by Barker and Fock, leads to a considerable improvement in the shape of the phase diagram and avoids some of the difficulties encountered in their calculation. Phase diagrams are displayed for various choices of the parameters: the number of contact points, the interaction potential, and the order of the approximation.

Computer Simulations Of Submicron Fib System Optics, W. Thompson, I. Honjo, Mark Utlaut

#### Computer Simulations Of Submicron Fib System Optics, W. Thompson, I. Honjo, Mark Utlaut

*Physics Faculty Publications and Presentations*

The design of the optical elements for a focused ion beam (FIB) system having a 50 mm spot size over a 1 mm square field requires extensive computational analysis. We discuss the mathematical techniques applied to the components of interest in this submicron FIB system; the electrostatic lenses, the mass analyzer, and the electrostatic deflectors. The results of ion trajectory calculations predicted for the whole FIB column by the computer code snow are presented. The aberration coefficients to third order and a parametric study of a stigmatic Wien filter whose design includes entrance and exit fringe field effects will be ...

Non-Perturbative Renormalisation Using Dimensional Regularisation: Applications To The Ε Expansion, A. J. Mckane, D. J. Wallace, O. F. De Alcantara Bonfim

#### Non-Perturbative Renormalisation Using Dimensional Regularisation: Applications To The Ε Expansion, A. J. Mckane, D. J. Wallace, O. F. De Alcantara Bonfim

*Physics Faculty Publications and Presentations*

We give a prescription for the one-loop renormalisation of the imaginary parts of vertex functions in *g*ø^{4}, which are generated when gR < 0 is non-perturbative in ɛ. This fixed point determines the imaginary parts of the critical exponents which are generated when ɛ < 0, and allows us to determine the high-order behaviour of the perturbation series in E for these exponents. The generalisation of these ideas to the O(n) symmetric g(ø^{2})^{2} model is also given.

Probability Densities And The Random Variable Transformation Theorem, John D. Ramshaw

#### Probability Densities And The Random Variable Transformation Theorem, John D. Ramshaw

*Physics Faculty Publications and Presentations*

D. T. Gillespie has recently derived and discussed a random variable transformation (RVT) theorem relating the joint probability densities of functionally dependent sets of random variables.....

It is hoped that the present discussion will help to disseminate this basic relation among a wider circle of nonspecialists.