Jim Agard: A Retrospective

The subject of illusion has been at the core of Jim’s work from the get-go. So when he serendipitously met some guy one night who was toying with a bent hanger, insisting Jim entertain him by seeing if he could visually make the wire cube turn inside out, Jim was captivated. Moving from side to side, as instructed, Jim experienced the cube floating on an invisible axis. He went rampant. Up until then, his work had implied illusion rather than created actual illusion. A chance encounter and his discovery of the Necker cube propelled him into what would become the basis of his life’s work. Like when one learns to open one’s eyes underwater for the first time, everything becomes wildly different, just knowing there is a whole other way of seeing. Jim’s work is purely non-objective and formal, yet equally laden with profound conceptual significance. It invites an approach that is lucid and straightforward, while encouraging a willingness to let the focus blur. To hold these views simultaneously. To see and then hyper-see and be willing to not see, and in not seeing, see even more. [excerpt]https://cupola.gettysburg.edu/artcatalogs/1003/thumbnail.jp

Massless Three Dimensional Quantum Electrodynamics and Thirring Model Constrained by Large Flavor Number

We explicitly prove that in three dimensional massless quantum electrodynamics at finite temperature, zero density and large number of flavors the number of infrared degrees of freedom is never larger than the corresponding number of ultraviolet. Such a result, strongly dependent on the asymptotic freedom of the theory, is reversed in three dimensional Thirring model due to the positive derivative of its running coupling constant

A comparative evaluation of anomaloscopes: Pickford-Nicholson & Nagel

Included among color vision testing instruments are the Nagel anomaloscope and the Pickford-Nicholson anomaloscope. The Nagel is a spectral instrument whereas the Pickford-Nicholson uses filters. This paper examines how closely the two instruments actually correspond. It is concluded that both instruments do quantitatively yield similar results on both normals and color deficients. The standard deviations of both the means and ranges on the two instruments are equal, at the .02 level of significance

Can Sigma Models Describe Finite Temperature Chiral Transitions?

Large-N expansions and computer simulations indicate that the universality class of the finite temperature chiral symmetry restoration transition in the 3D Gross-Neveu model is mean field theory. This is a counterexample to the standard 'sigma model' scenario which predicts the 2D Ising model universality class. We trace the breakdown of the standard scenario (dimensional reduction and universality) to the absence of canonical scalar fields in the model. We point out that our results could be generic for theories with dynamical symmetry breaking, such as Quantum Chromodynamics.Comment: 9 pages, 2 ps figure

Thermal fluctuations and disorder effects in vortex lattices

We calculate using loop expansion the effect of fluctuations on the structure function and magnetization of the vortex lattice and compare it with existing MC results. In addition to renormalization of the height of the Bragg peaks of the structure function, there appears a characteristic saddle shape ''halos'' around the peaks. The effect of disorder on magnetization is also calculated. All the infrared divergencies related to soft shear cancel.Comment: 10 pages, revtex file, one figur

Interpretations of Presburger Arithmetic in Itself

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201

Nature of 45 degree vortex lattice reorientation in tetragonal superconductors

The transformation of the vortex lattice in a tetragonal superconductor which consists of its 45 degree reorientation relative to the crystal axes is studied using the nonlocal London model. It is shown that the reorientation occurs as two successive second order (continuous) phase transitions. The transition magnetic fields are calculated for a range of parameters relevant for borocarbide superconductors in which the reorientation has been observed

The Dynamical Behaviors in (2+1)-Dimensional Gross-Neveu Model with a Thirring Interaction

We analyze (2+1)-dimensional Gross-Neveu model with a Thirring interaction, where a vector-vector type four-fermi interaction is on equal terms with a scalar-scalar type one. The Dyson-Schwinger equation for fermion self-energy function is constructed up to next-to-leading order in 1/N expansion. We determine the critical surface which is the boundary between a broken phase and an unbroken one in ($\alpha_c,~ \beta_c,~ N_c$) space. It is observed that the critical behavior is mainly controlled by Gross-Neveu coupling $\alpha_c$ and the region of the broken phase is separated into two parts by the line $\alpha_c=\alpha_c^*(=\frac{8}{\pi^2})$. The mass function is strongly dependent upon the flavor number N for $\alpha > \alpha_c^*$, while weakly for $\alpha \alpha_c^*$, the critical flavor number $N_c$ increases as Thirring coupling $\beta$ decreases. By driving the CJT effective potential, we show that the broken phase is energetically preferred to the symmetric one. We discuss the gauge dependence of the mass function and the ultra-violet property of the composite operators.Comment: 19 pages, LaTex, 6 ps figure files(uuencoded in seperate file

Equation of state for the 2+1 dimensional Gross-Neveu model at order 1/N

We calculate the equation of state of the Gross-Neveu model in 2+1 dimensions at order 1/N, where N is the number of fermion species. We make use of a general formula valid for four-fermion theories, previously applied to the model in 1+1 dimensions. We consider both the discrete and continuous symmetry versions of the model. We show that the pion-like excitations give the dominant contribution at low temperatures. The range of validity for such pion dominance is analyzed. The complete analysis from low to high temperatures also shows that in the critical region the role of composite states is relevant, even for quite large N, and that the free-component behaviour at high T starts at about twice the mean field critical temperature.Comment: 19 pages, RevTeX, 10 figures.p