A New Method of Calculating the Spin-Wave Velocity cc of Spin-1/2 Antiferromagnets With O(N)O(N) Symmetry in a Monte Carlo Simulation

Motivated by the so-called cubical regime in magnon chiral perturbation theory, we propose a new method to calculate the low-energy constant, namely the spin-wave velocity $c$ of spin-1/2 antiferromagnets with $O(N)$ symmetry in a Monte Carlo simulation. Specifically we suggest that $c$ can be determined by $c = L/\beta$ when the squares of the spatial and temporal winding numbers are tuned to be the same in the Monte Carlo calculations. Here $\beta$ and $L$ are the inverse temperature and the box size used in the simulations when this condition is met. We verify the validity of this idea by simulating the quantum spin-1/2 XY model. The $c$ obtained by using the squares of winding numbers is given by $c = 1.1348(5)Ja$ which is consistent with the known values of $c$ in the literature. Unlike other conventional approaches, our new idea provides a direct method to measure $c$. Further, by simultaneously fitting our Monte Carlo data of susceptibilities $\chi_{11}$ and spin susceptibilities $\chi$ to their theoretical predictions from magnon chiral perturbation theory, we find $c$ is given by $c = 1.1347(2)Ja$ which agrees with the one we obtain by the new method of using the squares of winding numbers. The low-energy constants magnetization density ${\cal M}$ and spin stiffenss $\rho$ of quantum spin-1/2 XY model are determined as well and are given by ${\cal M} = 0.43561(1)/a^2$ and $\rho = 0.26974(5)J$, respectively. Thanks to the prediction power of magnon chiral perturbation theory which puts a very restricted constraint among the low-energy constants for the model considered here, the accuracy of ${\cal M}$ we present in this study is much precise than previous Monte Carlo result.Comment: 5 pages, 7 figure

Mapping cyberspace: visualising, analysing and exploring virtual worlds

In the past years, with the development of computer networks such as the Internet and world wide web (WWW), cyberspace has been increasingly studied by researchers in various disciplines such as computer sciences, sociology, geography, and cartography as well. Cyberspace is mainly rooted in two computer technologies: network and virtual reality. Cybermaps, as special maps for cyberspace, have been used as a tool for understanding various aspects of cyberspace. As recognised, cyberspace as a virtual space can be distinguished from the earth we live on in many ways. Because of these distinctions, mapping it implies a big challenge for cartographers with their long tradition of mapping things in clear ways. This paper, by comparing it to traditional maps, addresses various cybermap issues such as visualising, analysing and exploring cyberspace from different aspects

Acceleration computing process in wavelength scanning interferometry

The optical interferometry has been widely explored for surface measurement due to the advantages of non-contact and high accuracy interrogation. Eventually, some interferometers are used to measure both rough and smooth surfaces such as white light interferometry and wavelength scanning interferometry (WSI). The WSI can be used to measure large discontinuous surface profiles without the phase ambiguity problems. However, the WSI usually needs to capture hundreds of interferograms at different wavelength in order to evaluate the surface finish for a sample. The evaluating process for this large amount of data needs long processing time if CPUs traditional programming is used. This paper presents a parallel programming model to achieve the data parallelism for accelerating the computing analysis of the captured data. This parallel programming is based on CUDATM C program structure that developed by NVIDIA. Additionally, this paper explains the mathematical algorithm that has been used for evaluating the surface profiles. The computing time and accuracy obtained from CUDA program, using GeForce GTX 280 graphics processing unit (GPU), were compared to those obtained from sequential execution Matlab program, using Intel® Core™2 Duo CPU. The results of measuring a step height sample shows that the parallel programming capability of the GPU can highly accelerate the floating point calculation throughput compared to multicore CPU

Very High Precision Determination of Low-Energy Parameters: The 2-d Heisenberg Quantum Antiferromagnet as a Test Case

The 2-d spin 1/2 Heisenberg antiferromagnet with exchange coupling $J$ is investigated on a periodic square lattice of spacing $a$ at very small temperatures using the loop-cluster algorithm. Monte Carlo data for the staggered and uniform susceptibilities are compared with analytic results obtained in the systematic low-energy effective field theory for the staggered magnetization order parameter. The low-energy parameters of the effective theory, i.e.\ the staggered magnetization density ${\cal M}_s = 0.30743(1)/a^2$, the spin stiffness $\rho_s = 0.18081(11) J$, and the spin wave velocity $c = 1.6586(3) J a$ are determined with very high precision. Our study may serve as a test case for the comparison of lattice QCD Monte Carlo data with analytic predictions of the chiral effective theory for pions and nucleons, which is vital for the quantitative understanding of the strong interaction at low energies.Comment: 5 pages, 4 figures, 1 tabl

Investigation of a universal behavior between N\'eel temperature and staggered magnetization density for a three-dimensional quantum antiferromagnet

We simulate the three-dimensional quantum Heisenberg model with a spatially anisotropic ladder pattern using the first principles Monte Carlo method. Our motivation is to investigate quantitatively the newly established universal relation $T_N/\sqrt{c^3}$ $\propto$ ${\cal M}_s$ near the quantum critical point (QCP) associated with dimerization. Here $T_N$, $c$, and ${\cal M}_s$ are the N\'eel temperature, the spinwave velocity, and the staggered magnetization density, respectively. For all the physical quantities considered here, such as $T_N$ and ${\cal M}_s$, our Monte Carlo results agree nicely with the corresponding results determined by the series expansion method. In addition, we find it is likely that the effect of a logarithmic correction, which should be present in (3+1)-dimensions, to the relation $T_N/\sqrt{c^3}$ $\propto$ ${\cal M}_s$ near the investigated QCP only sets in significantly in the region with strong spatial anisotropy.Comment: 5 pages, 7 figures, 2 table