High precision single-cluster Monte Carlo measurement of the critical exponents of the classical 3D Heisenberg model

We report measurements of the critical exponents of the classical three-dimensional Heisenberg model on simple cubic lattices of size $L^3$ with $L$ = 12, 16, 20, 24, 32, 40, and 48. The data was obtained from a few long single-cluster Monte Carlo simulations near the phase transition. We compute high precision estimates of the critical coupling $K_c$, Binder's parameter $U^* and the critical exponents$\nu,\beta / \nu, \eta$, and$\alpha / \nu$, using extensively histogram reweighting and optimization techniques that allow us to keep control over the statistical errors. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition as compared to local update algorithms. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.Comment: 4 pages, (contribution to the Lattice92 proceedings) 1 postscript file as uufile included. Preprints FUB-HEP 21/92 and HLRZ 89/92. (note: first version arrived incomplete due to mailer problems

Finite-Size Scaling Study of the Three-Dimensional Classical Heisenberg Model

We use the single-cluster Monte Carlo update algorithm to simulate the three-dimensional classical Heisenberg model in the critical region on simple cubic lattices of size $L^3$ with $L=12, 16, 20, 24, 32, 40$, and $48$. By means of finite-size scaling analyses we compute high-precision estimates of the critical temperature and the critical exponents, using extensively histogram reweighting and optimization techniques. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.Comment: 9 pages, FUB-HEP 9/92, HLRZ Preprint 56/92, August 199

Three-State Anti-ferromagnetic Potts Model in Three Dimensions: Universality and Critical Amplitudes

We present the results of a Monte Carlo study of the three-dimensional anti-ferromagnetic 3-state Potts model. We compute various cumulants in the neighbourhood of the critical coupling. The comparison of the results with a recent high statistics study of the 3D XY model strongly supports the hypothesis that both models belong to the same universality class. From our numerical data for the anti-ferromagnetic 3-state Potts model we obtain for the critical coupling \coup_c=0.81563(3), and for the static critical exponents $\gamma /\nu=1.973(9)$ and $\nu=0.664(4)$.Comment: 18pages + 3figures, KL-TH-94/5 , CERN-TH.7183/9

Critical Behaviour of the 3D XY-Model: A Monte Carlo Study

We present the results of a study of the three-dimensional $XY$-model on a simple cubic lattice using the single cluster updating algorithm combined with improved estimators. We have measured the susceptibility and the correlation length for various couplings in the high temperature phase on lattices of size up to $L=112$. At the transition temperature we studied the fourth-order cumulant and other cumulant-like quantities on lattices of size up to $L=64$. From our numerical data we obtain for the critical coupling \coup_c=0.45420(2), and for the static critical exponents $\gamma /\nu=1.976(6)$ and $\nu=0.662(7)$.Comment: 24 pages (4 PS-Figures Not included, Revtex 3.O file), report No.: CERN-TH.6885/93, KL-TH-93/1

Finite size effects on measures of critical exponents in d=3 O(N) models

We study the critical properties of three-dimensional O(N) models, for N=2,3,4. Parameterizing the leading corrections-to-scaling for the $\eta$ exponent, we obtain a reliable infinite volume extrapolation, incompatible with previous Monte Carlo values, but in agreement with $\epsilon$-expansions. We also measure the critical exponent related with the tensorial magnetization as well as the $\nu$ exponents and critical couplings.Comment: 12 pages, 2 postscript figure

Flat Choroidal Nevus Inaccessible to Ultrasound Sonography Evaluated by Enhanced Depth Imaging Optical Coherence Tomography

Purpose: To demonstrate the usefulness of enhanced depth imaging optical coherence tomography (EDI-OCT) in investigating choroidal lesions inaccessible to ultrasound sonography. Methods: In a 60-year-old woman with an asymptomatic choroidal nevus, normal OCT was used to observe the macula and EDI-OCT to image the choroidal nevus that was inaccessible to ultrasound. The exact location of the lesion in the choroid and the dimensions of the nevus were measured. Results: The lesion was located in the superior macula, and the nevus was homogeneous in its reflectivity. We observed a thickened choroid delineated by the shadow cone behind it, measuring 1,376 × 325 µm in the larger vertical cut and 1,220 × 325 µm in the larger horizontal cut in an image with a 1:1 pixel mapping and automatic zoom. The macular profile and thickness were both normal. Conclusions: EDI-OCT appears to be an excellent technique for measuring choroidal nevi and all choroidal lesions accessible to OCT imaging by depicting their exact location in the choroid, their dimensions, and their demarcation from the surrounding healthy tissue, thus allowing for a more efficient and accurate follow-up

Random Bond Potts Model: the Test of the Replica Symmetry Breaking

Averaged spin-spin correlation function squared $\overline{^{2}}$ is calculated for the ferromagnetic random bond Potts model. The technique being used is the renormalization group plus conformal field theory. The results are of the $\epsilon$ - expansion type fixed point calculation, $\epsilon$ being the deviation of the central charge (or the number of components) of the Potts model from the Ising model value. Calculations are done both for the replica symmetric and the replica symmetry broken fixed points. The results obtained allow for the numerical simulation tests to decide between the two different criticalities of the random bond Potts model.Comment: 50 pages, Latex, 2 eps figure

Critical Exponents of the Classical 3D Heisenberg Model: A Single-Cluster Monte Carlo Study

We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors. In one set of simulations we employ the usual finite-size scaling methods to compute the critical exponents $\nu,\alpha,\beta,\gamma, \eta$ from a few measurements in the vicinity of the critical point, making extensive use of histogram reweighting and optimization techniques. In another set of simulations we report measurements of improved estimators for the spatial correlation length and the susceptibility in the high-temperature phase, obtained on lattices with up to $100^3$ spins. This enables us to compute independent estimates of $\nu$ and $\gamma$ from power-law fits of their critical divergencies.Comment: 33 pages, 12 figures (not included, available on request). Preprint FUB-HEP 19/92, HLRZ 77/92, September 199