Universality and the five-dimensional Ising model

We solve the long-standing discrepancy between Monte Carlo results and the renormalization prediction for the Binder cumulant of the five-dimensional Ising model. Our conclusions are based on accurate Monte Carlo data for systems with linear sizes up to L=22. A detailed analysis of the corrections to scaling allows the extrapolation of these results to L=\infinity. Our determination of the critical point, K_c=0.1139150 (4), is more than an order of magnitude more accurate than previous estimates.Comment: 6 pages LaTeX, 1 PostScript figure. Uses cite.sty (included) and epsf.sty. Also available as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm

Critical Surface Free Energies and Universal Finite-Size Scaling Amplitudes of Three-Dimensional XY Models by Direct Monte Carlo Sampling

Direct Monte Carlo sampling is employed to obtain estimates of excess surface free energies of three-dimensional XY models at criticality. Results for simple-cubic and body-centered-cubic lattices are consistent with universality of finite-size scaling amplitudes. The results are used to estimate the magnitude of the thinning effect, mediated by the incipient long-ranged correlations, on liquid-helium films at the λ point

Surface Free Energies of Three-Dimensional Ising Models and Universality of Finite-Size Scaling Amplitudes by Direct Monte Carlo Sampling

Direct Monte Carlo sampling is employed to obtain estimates of excess surface free energies of three-dimensional Ising models at criticality. Results for simple and body-centered-cubic lattices provide strong evidence for the universality of finite-size scaling amplitudes and in particular the related interaction per unit area, mediated via the incipient long-ranged correlations, of two free surfaces a finite distance apart

Thermodynamics predicts how confinement modifies hard-sphere dynamics

We study how confining the equilibrium hard-sphere fluid to restrictive one- and two-dimensional channels with smooth interacting walls modifies its structure, dynamics, and entropy using molecular dynamics and transition-matrix Monte Carlo simulations. Although confinement strongly affects local structuring, the relationships between self-diffusivity, excess entropy, and average fluid density are, to an excellent approximation, independent of channel width or particle-wall interactions. Thus, thermodynamics can be used to predict how confinement impacts dynamics.Comment: 4 pages, 4 figure

RIP INPUT TABLES FROM WAPDEG FOR LA DESIGN SELECTION: ENHANCED DESIGN ALTERNATIVE V

The purpose of this calculation is to document (1) the Waste Package Degradation (WAPDEG) version 3.09 (CRWMS M&O 1998b, Software Routine Report for WAPDEG (Version 3.09)) simulations used to analyze degradation and failure of 2-cm thick titanium grade 7 corrosion resistant material (CRM) drip shields (that are placed over waste packages composed of a 2-cm thick Alloy 22 corrosion resistant material (CRM) as the outer barrier and an unspecified material to provide structural support as the inner barrier) as well as degradation and failure of the waste packages themselves, and (2) post-processing of these results into tables of drip shield/waste package degradation time histories suitable for use as input into the Integrated Probabilistic Simulator for Environmental Systems (RIP) version 5.19.01 (Golder Associates 1998) computer code. Performance credit of the inner barrier material is not taken in this calculation. This calculation supports Performance Assessment analysis of the License Application Design Selection (LADS) Enhanced Design Alternative V. Additional details concerning the Enhanced Design Alternative V are provided in a Design Input Request (CRWMS M&O 1999e, Design Input Request for LADS Phase II EDA Evaluations, Item 3)

Removal of Singularities from Taylor Series

A mathematical procedure is described whereby the radius of convergence of a Taylor series can be increased through the inclusion of complex poles in a rational approximation. Computer results show that this technique is quite independent of the asymptotic limit of the power series and only depends on the positions of the singularities. Aside from the applications in one variable, this method vastly improves perturbative solutions to symplectic, dynamical mappings in many dimensions by removing resonances in the complex plane

Spectral statistics of the k-body random-interaction model

We reconsider the question of the spectral statistics of the k-body random-interaction model, investigated recently by Benet, Rupp, and Weidenmueller, who concluded that the spectral statistics are Poissonian. The binary-correlation method that these authors used involves formal manipulations of divergent series. We argue that Borel summation does not suffice to define these divergent series without further (arbitrary) regularization, and that this constitutes a significant gap in the demonstration of Poissonian statistics. Our conclusion is that the spectral statistics of the k-body random-interaction model remains an open question.Comment: 17 pages, no figure

Properties of Interfaces in the two and three dimensional Ising Model

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the $2D$ and $3D$ Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability density. Stringent tests of the numerical methods are performed by reproducing with high precision exact $2D$ results. In the physically more interesting $3D$ case we estimate the amplitude $F^s_0$ of the critical interfacial tension $F^s = F^s_0 t^\mu$ to be $F^s_0 = 1.52 \pm 0.05$. This result is in good agreement with a previous MC calculation by Mon, as well as with experimental results for related amplitude ratios. In addition, we study in some details the shape of the magnetic probability density for temperatures below the Curie point.Comment: 25 pages; sorry no figures include

RIP Input Tables From Wapdeg For La Design Selection: Enhanced Design Alternative Iiib

The purpose of this calculation is to document the Waste Package Degradation (WAPDEG) version 3.09 (CRWMS M&O 1998b. 'Software Routine Report for WAPDEG' (Version 3.09)) simulations used to analyze degradation and failure of 2-cm thick titanium grade 7 corrosion resistant material (CRM) drip shields as well as degradation and failure of the waste packages over which they are placed. The waste packages are composed of two corrosion resistant materials (CRM) barriers. The outer barrier is composed of 2 cm of Alloy 22 and the inner barrier is composed of 1.5 cm of titanium grade 7. The WAPDEG simulation results are post-processed into tables of drip shield/waste package degradation time histories suitable for use as input into the Integrated Probabilistic Simulator for Environmental Systems (RIP) version 5.19.01 (Golder Associates 1998) computer code. This calculation supports Performance Assessment analysis of the License Application Design Selection (LADS) Enhanced Design Alternative IIIb

Binomial level densities

It is shown that nuclear level densities in a finite space are described by a continuous binomial function, determined by the first three moments of the Hamiltonian, and the dimensionality of the underlying vector space. Experimental values for $^{55}$Mn, $^{56}$Fe, and $^{60}$Ni are very well reproduced by the binomial form, which turns out to be almost perfectly approximated by Bethe's formula with backshift. A proof is given that binomial densities reproduce the low moments of Hamiltonians of any rank: A strong form of the famous central limit result of Mon and French. Conditions under which the proof may be extended to the full spectrum are examined.Comment: 4 pages 2 figures Second version (previous not totally superseeded