Verification of Snapshotable Trees using Access Permissions and Typestate

Abstract. We use access permissions and typestate to specify and verify a Java library that implements snapshotable search trees, as well as some client code. We formalize our approach in the Plural tool, a sound modular typestate checking tool. We describe the challenges to verifying snapshotable trees in Plural, give an abstract interface specification against which we verify the client code, provide a concrete specification for an implementation and describe proof patterns we found. We also relate this verification approach to other techniques used to verify this data structure.

Finite Size Scaling and ``perfect'' actions: the three dimensional Ising model

Using Finite-Size Scaling techniques, we numerically show that the first irrelevant operator of the lattice $\lambda\phi^4$ theory in three dimensions is (within errors) completely decoupled at $\lambda=1.0$. This interesting result also holds in the Thermodynamical Limit, where the renormalized coupling constant shows an extraordinary reduction of the scaling-corrections when compared with the Ising model. It is argued that Finite-Size Scaling analysis can be a competitive method for finding improved actions.Comment: 13 pages, 3 figure

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

Bethe--Salpeter equation in QCD

We extend to regular QCD the derivation of a confining $q \bar{q}$ Bethe--Salpeter equation previously given for the simplest model of scalar QCD in which quarks are treated as spinless particles. We start from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by ${1\over m^2}$ expansion the corresponding Wilson loop potential can be reobtained, spin--dependent and velocity--dependent terms included. We also show that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.Comment: 23 pages, revte

Finite one dimensional impenetrable Bose systems: Occupation numbers

Bosons in the form of ultra cold alkali atoms can be confined to a one dimensional (1d) domain by the use of harmonic traps. This motivates the study of the ground state occupations $\lambda_i$ of effective single particle states $\phi_i$, in the theoretical 1d impenetrable Bose gas. Both the system on a circle and the harmonically trapped system are considered. The $\lambda_i$ and $\phi_i$ are the eigenvalues and eigenfunctions respectively of the one body density matrix. We present a detailed numerical and analytic study of this problem. Our main results are the explicit scaled forms of the density matrices, from which it is deduced that for fixed $i$ the occupations $\lambda_i$ are asymptotically proportional to $\sqrt{N}$ in both the circular and harmonically trapped cases.Comment: 22 pages, 8 figures (.eps), uses REVTeX

Star-graph expansions for bond-diluted Potts models

We derive high-temperature series expansions for the free energy and the susceptibility of random-bond $q$-state Potts models on hypercubic lattices using a star-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength $p$ as well as the dimension $d$ as symbolic parameters. By applying several series analysis techniques to the new series expansions, one can scan large regions of the $(p,d)$ parameter space for any value of $q$. For the bond-diluted 4-state Potts model in three dimensions, which exhibits a rather strong first-order phase transition in the undiluted case, we present results for the transition temperature and the effective critical exponent $\gamma$ as a function of $p$ as obtained from the analysis of susceptibility series up to order 18. A comparison with recent Monte Carlo data (Chatelain {\em et al.}, Phys. Rev. E64, 036120(2001)) shows signals for the softening to a second-order transition at finite disorder strength.Comment: 8 pages, 6 figure

Confining QCD Strings, Casimir Scaling, and a Euclidean Approach to High-Energy Scattering

We compute the chromo-field distributions of static color-dipoles in the fundamental and adjoint representation of SU(Nc) in the loop-loop correlation model and find Casimir scaling in agreement with recent lattice results. Our model combines perturbative gluon exchange with the non-perturbative stochastic vacuum model which leads to confinement of the color-charges in the dipole via a string of color-fields. We compute the energy stored in the confining string and use low-energy theorems to show consistency with the static quark-antiquark potential. We generalize Meggiolaro's analytic continuation from parton-parton to gauge-invariant dipole-dipole scattering and obtain a Euclidean approach to high-energy scattering that allows us in principle to calculate S-matrix elements directly in lattice simulations of QCD. We apply this approach and compute the S-matrix element for high-energy dipole-dipole scattering with the presented Euclidean loop-loop correlation model. The result confirms the analytic continuation of the gluon field strength correlator used in all earlier applications of the stochastic vacuum model to high-energy scattering.Comment: 65 pages, 13 figures, extended and revised version to be published in Phys. Rev. D (results unchanged, 2 new figures, 1 new table, additional discussions in Sec.2.3 and Sec.5, new appendix on the non-Abelian Stokes theorem, old Appendix A -> Sec.3, several references added

Single-crystal Ih Ice Surfaces Unveil Connection between Macroscopic and Molecular Structure

Physics and chemistry of ice surfaces are not only of fundamental interest but also have important impacts on biological and environmental processes. As ice surfaces—particularly the two prism faces—come under greater scrutiny, it is increasingly important to connect the macroscopic faces with the molecular-level structure. The microscopic structure of the ubiquitous ice Ih crystal is well-known. It consists of stacked layers of chair-form hexagonal rings referred to as molecular hexagons. Crystallographic unit cells can be assembled into a regular right hexagonal prism. The bases are labeled crystallographic hexagons. The two hexagons are rotated 30° with respect to each other. The linkage between the familiar macroscopic shape of hexagonal snowflakes and either hexagon is not obvious per se. This report presents experimental data directly connecting the macroscopic shape of ice crystals and the microscopic hexagons. Large ice single crystals were used to fabricate samples with the basal, primary prism, or secondary prism faces exposed at the surface. In each case, the same sample was used to capture both a macroscopic etch pit image and an electron backscatter diffraction (EBSD) orientation density function (ODF) plot. Direct comparison of the etch pit image and the ODF plot compellingly connects the macroscopic etch pit hexagonal profile to the crystallographic hexagon. The most stable face at the ice–water interface is the smallest area face at the ice–vapor interface. A model based on the molecular structure of the prism faces accounts for this switch

Casimir scaling of SU(3) static potentials

Potentials between static colour sources in eight different representations are computed in four dimensional SU(3) gauge theory. The simulations have been performed with the Wilson action on anisotropic lattices where the renormalised anisotropies have been determined non-perturbatively. After an extrapolation to the continuum limit we are able to exclude any violations of the Casimir scaling hypothesis that exceed 5% for source separations of up to 1 fm.Comment: 12 pages, 10 figures, RevTeX, v2: 1 reference added, more explanation about advantages of anisotrop