Bulletin of the American Physical Society
2014 Annual Fall Meeting of the APS Ohio-Region Section
Volume 59, Number 13
Friday–Saturday, October 24–25, 2014; Portsmouth, Ohio
Session G1: Condensed Matter, Nuclear and Other Physics |
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Chair: Jerry Ross, Shawnee State University Room: University Center 215 |
Saturday, October 25, 2014 9:30AM - 9:42AM |
G1.00001: Magnetic Phase Diagram of a 2D $XY$ Model with Random Easy Axis Orientation Donald Priour Using Monte Carlo simulations, we examine the bulk magnetic behavior of classical $XY$ models with a inherently random anisotropy manifested as a randomly oriented easy axis for each pair of interacting spins in the 2D square lattice with magnetic interactions among nearest neighbor spins. Whereas thermally excited spin waves destroy ferromagnetic order in the isotropic $XY$ model for any finite temperature, long-range spin alignment is very effectively stabilized in $XY$ models with collinear easy axes. We examine the extent to which ferromagnetic order is supported for the disordered counterpart with randomly oriented easy axis directions. With Binder cumulants and finite size scaling analyses, we determine the phase diagram for a variety of values of the anisotropy parameter $\gamma$, directly related to the relative energetic favorability of alignment along the direction of preferred spin orientation. We consider the possibility of ferromagnetic order for values of $\gamma$ in the intermediate regime, in principle strong enough to imbue spin waves with a finite energy yet weak enough to avoid a non-ferromagnetic ground state. [Preview Abstract] |
Saturday, October 25, 2014 9:42AM - 9:54AM |
G1.00002: Revisiting the RKKY interaction with a polarized electron gas Christopher Porter The RKKY interaction is a well-known itinerant interaction that can account for long-range magnetic interaction, and does not require overall polarization of the electron gas through which the interaction occurs. In fact, very few authors have considered the effects of the polarization of the electron gas. We revisit the general form of the pairwise RKKY interaction, including the possibility of a polarized electron gas. A few special cases in bulk materials are considered, in which the effect of electron gas polarization on magnetic interactions is analytically calculable. We also present preliminary results of classical Monte Carlo calculations. Such calculations are appropriate for disordered distributions of large-spin ions in a nonmagnetic lattice such as the heavy doping of Mn in GaAs diluted magnetic semiconductors. [Preview Abstract] |
Saturday, October 25, 2014 9:54AM - 10:06AM |
G1.00003: Thickness-Controlled Synthesis of Colloidal PbS Nanosheets and Their Thickness-Dependent Energy Gaps. Zhoufeng Jiang, Kamal Subedi, Ghadendra Bhandari, Yufan He, Matthew Leopold, Nick Reilly, H. Peter Lu, Alexey Zayak, Liangfeng Sun Ultrathin colloidal PbS nanosheets are synthesized using organometallic precursors with chloroalkane cosolvents, resulting in tunable thicknesses ranging from 1.2 nm to 4.6 nm. Corresponding photoluminescence peaks are tuned from 1470 nm to 2175 nm. The one-dimensional confinement energy of these quasi-two-dimensional nanosheets is found to be proportional to 1/L instead of 1/L$^2$ (L is the thickness of the nanosheet), which is consistent with results calculated using density functional theory. [Preview Abstract] |
Saturday, October 25, 2014 10:06AM - 10:18AM |
G1.00004: Spinodal Field and Surface Free Energy of the Ising Model on the \{5,4\} Tiling of the Hyperbolic Plane Howard L. Richards Consider the ferromagnetic Ising model on a two-dimensional lattice, with all the spins initially \textit{up} but with a weak \textit{down} magnetic field, evolving under a single-spin-flip Metropolis dynamic. If the lattice lies in the Euclidean plane -- for example, if it is the square lattice --- a droplet of \textit{down} spins (appearing as a thermal excitation) can decrease the free energy of the system by growing if it is larger than a finite critical size. In the hyperbolic plane, however, beneath a \textbf{spinodal field} $H_{sp}$ it is impossible to nucleate a critical droplet. Monte Carlo simulations for finite regions of the \{5,4\} tiling with mean-field boundary conditions show that $H_{sp}^{2/3}$ is approximately a linear function of temperature, which should be expected at least in the neighborhood of the critical temperature. Assuming that the droplets are circular, a first estimate of the surface free energy can be made. [Preview Abstract] |
Saturday, October 25, 2014 10:18AM - 10:30AM |
G1.00005: Approximate Solution of the Time-Independent Schr\"{o}dinger Equation for the Quartic Oscillator Ulrich Zurcher, Luke Baker Exact solutions to the quantum quartic oscillator are not known. We equip the set of Hamiltonian operators with a metric, thereby providing a notion of distance between these operators. This metric is a generalization of the $L^{2}$ metric on the space of Lebesgue measurable functions. We determine Hamiltonian operators with known solutions (to the Scr\"{o}dinger equation), and then use the generalized metric to find a unique Hamiltonian with known solutions that is minimal in distance to the quartic Hamiltonian. The Hamiltonian that we seek is, in fact, the Hamiltonian of the harmonic oscillator. Minimizing the distance will correspondingly suggest a harmonic frequency. The approximate solutions to the quartic oscillator will thus be the solutions of the harmonic oscillator with the suggested frequency. [Preview Abstract] |
Saturday, October 25, 2014 10:30AM - 10:42AM |
G1.00006: Estakhr Permutation Amplitude, (String Theory) Ahmad Reza Estakhr Permutation $P(n,m)=\frac{n!}{(n- m)!}$, when interpreted as a scattering amplitude, has many of the features needed to explain the physical properties of strongly interacting mesons, such as symmetry and duality. The formula is the following: $P(\frac{1}{2}(k_1+k_2)^2-2,\frac {-1}{2}(k_2+k_3)^2+1)P(\frac{1}{2} (k_2+k_3)^2-2,\frac{1}{2} (k_2+k_3)^2-2)$, k$^{n}$ is a vector (such as a four- vector) referring to the momentum of the n$^{th}$ particle. relashionship between Euler beta function and Permutation: $B(n,m)=P(n-1,-m)P(m-1,m-1)$, Relationship between the Veneziano amplitude and Estakhr Permutation Amplitude: $B(\frac{1}{2}(k_1+k_2)^2-1,\frac {1}{2}(k_2+k_3)^2-1)=P(\frac{1}{2} (k_1+k_2)^2-2,\frac{-1}{2} (k_2+k_3)^2+1)P(\frac{1}{2} (k_2+k_3)^2-2,\frac{1}{2} (k_2+k_3)^2-2)$, (The notion of permutation relates to act of permuting or rearranging members of a set into a particular sequence or order) [Preview Abstract] |
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