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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.

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.