Non-Coexistence of Infinite Clusters in Two-Dimensional Dependent Site Percolation

This paper presents three results on dependent site percolation on the square lattice. First, there exists no positively associated probability measure on {0,1}^{Z^2} with the following properties: a) a single infinite 0cluster exists almost surely, b) at most one infinite 1*cluster exists almost surely, c) some probabilities regarding 1*clusters are bounded away from zero. Second, we show that coexistence of an infinite 1*cluster and an infinite 0cluster is almost surely impossible when the underlying probability measure is ergodic with respect to translations, positively associated, and satisfies the finite energy condition. The third result analyses the typical structure of infinite clusters of both types in the absence of positive association. Namely, under a slightly sharpened finite energy condition, the existence of infinitely many disjoint infinite self-avoiding 1*paths follows from the existence of an infinite 1*cluster. The same holds with respect to 0paths and 0clusters.Comment: 17 pages, 1 figur

First-order transitions for some generalized XY models

In this note we demonstrate the occurrence of first-order transitions in temperature for some recently introduced generalized XY models, and also point out the connection between them and annealed site-diluted (lattice-gas) continuous-spin models

Canted antiferromagnetism in phase-pure CuMnSb

We report the low-temperature properties of phase-pure single crystals of the half-Heusler compound CuMnSb grown by means of optical float-zoning. The magnetization, specific heat, electrical resistivity, and Hall effect of our single crystals exhibit an antiferromagnetic transition at $T_{\mathrm{N}} = 55~\mathrm{K}$ and a second anomaly at a temperature $T^{*} \approx 34~\mathrm{K}$. Powder and single-crystal neutron diffraction establish an ordered magnetic moment of $(3.9\pm0.1)~\mu_{\mathrm{B}}/\mathrm{f.u.}$, consistent with the effective moment inferred from the Curie-Weiss dependence of the susceptibility. Below $T_{\mathrm{N}}$, the Mn sublattice displays commensurate type-II antiferromagnetic order with propagation vectors and magnetic moments along $\langle111\rangle$ (magnetic space group $R[I]3c$). Surprisingly, below $T^{*}$, the moments tilt away from $\langle111\rangle$ by a finite angle $\delta \approx 11^{\circ}$, forming a canted antiferromagnetic structure without uniform magnetization consistent with magnetic space group $C[B]c$. Our results establish that type-II antiferromagnetism is not the zero-temperature magnetic ground state of CuMnSb as may be expected of the face-centered cubic Mn sublattice.Comment: 14 pages, 15 figure

Skyrmion Lattice in a Chiral Magnet

Skyrmions represent topologically stable field configurations with particle-like properties. We used neutron scattering to observe the spontaneous formation of a two-dimensional lattice of skyrmion lines, a type of magnetic vortices, in the chiral itinerant-electron magnet MnSi. The skyrmion lattice stabilizes at the border between paramagnetism and long-range helimagnetic order perpendicular to a small applied magnetic field regardless of the direction of the magnetic field relative to the atomic lattice. Our study experimentally establishes magnetic materials lacking inversion symmetry as an arena for new forms of crystalline order composed of topologically stable spin states

Selection Rules for One- and Two-Photon Absorption by Excitons in Carbon Nanotubes

Recent optical absorption/emission experiments showed that the lower energy optical transitions in carbon nanotubes are excitonic in nature, as predicted by theory. These experiments were based on the symmetry aspects of free electron-hole states and bound excitonic states. The present work shows, however, that group theory does not predict the selection rules needed to explain the two photon experiments. We obtain the symmetries and selection rules for the optical transitions of excitons in single-wall carbon nanotubes within the approach of the group of the wavevector, thus providing important information for the interpretation of theoretical and experimental optical spectra of these materials.Comment: 4 pages, 1 figure, 1 tabl

Poisson approximations for the Ising model

A $d$-dimensional Ising model on a lattice torus is considered. As the size $n$ of the lattice tends to infinity, a Poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration, provided the magnetic field $a=a(n)$ tends to $-\infty$ and the pair potential $b$ remains fixed. Using the Stein-Chen method, a bound is given for the total variation error in the ferromagnetic case.Comment: 25 pages, 1 figur

Conditional Intensity and Gibbsianness of Determinantal Point Processes

The Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and satisfy a bound implying stochastic domination by a Poisson point process. We also show that determinantal point processes satisfy the so-called condition $(\Sigma_{\lambda})$ which is a general form of Gibbsianness. Under a continuity assumption, the Gibbsian conditional probabilities can be identified explicitly.Comment: revised and extende

Translation-invariance of two-dimensional Gibbsian point processes

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with the special case of pure hard core repulsion in order to show how to treat hard cores in general.Comment: 44 pages, 6 figure

Thermodynamics for spatially inhomogeneous magnetization and Young-Gibbs measures

We derive thermodynamic functionals for spatially inhomogeneous magnetization on a torus in the context of an Ising spin lattice model. We calculate the corresponding free energy and pressure (by applying an appropriate external field using a quadratic Kac potential) and show that they are related via a modified Legendre transform. The local properties of the infinite volume Gibbs measure, related to whether a macroscopic configuration is realized as a homogeneous state or as a mixture of pure states, are also studied by constructing the corresponding Young-Gibbs measures