Exact low-temperature properties of a class of highly frustrated Hubbard models

We study the repulsive Hubbard model both analytically and numerically on a family of highly frustrated lattices which have one-electron states localized on isolated trapping cells. We construct and count exact many-electron ground states for a wide range of electron densities and obtain closed-form expressions for the low-temperature thermodynamic quantities. Furthermore, we find that saturated ferromagnetism is obtained only for sufficiently high electron densities and large Hubbard repulsion $U$ while there is no finite average moment in the ground states at lower densities.Comment: 8 pages, 7 figures, accepted for publication in Phys. Rev.

Lanczos Study of the S=1/2 Frustrated Square-Lattice Antiferromagnet in a Magnetic Field

We study the zero-temperature phase diagram of the frustrated square-lattice S=1/2 antiferromagnet in an external magnetic field numerically with the Lanczos algorithm. For strong frustration, we find disordered phases at high (and low) magnetic fields. Between these two disordered phases we find a plateau in the magnetization curve at half of the saturation magnetization which corresponds to a state with up-up-up-down (uuud) spin order. This and other considerations [cond-mat/0003343] suggest an unusual ordering scenario: There are an ordered phase with a spin gap (the plateau) and disordered magnetically gapless phases above and below. The transition to saturation is studied in further detail and problematic conclusions in earlier investigations of this region are pointed out.Comment: 4 pages REVTeX, 5 PostScript figures included using psfig.sty; submitted to the proceedings of the conference Highly Frustrated Magnetism 2000, Waterloo, June 11-15, 2000 (to appear in Canadian Journal of Physics

Towards exact field theory results for the Standard Model on fractional D6-branes

Fractional D6-branes on toroidal orbifold backgrounds are known to be able to accommodate the particle spectrum and gauge group of the Standard Model, but up to now exact results for their low-energy effective action are missing. Here we discuss how the conceptual ansatz of matching the string theoretic gauge couplings at one-loop with the supergravity expressions is generalised from the six-torus to orbifold backgrounds on which the Standard Model spectrum can be realised on fractional D6-branes. The Kaehler metrics and perturbatively exact holomorphic gauge kinetic functions can be classified in terms of the vanishing of some intersection angle and the related beta function coefficients, which potentially opens the possibility to extrapolate to smooth Calabi-Yau backgrounds.Comment: 1+3 pages, 2 tables; proceedings of the EPS-HEP 2011 conference in Grenoble 21-27 July 2011; v2: introduction and conclusion extended, published versio

Magnetocaloric effect in two-dimensional spin-1/2 antiferromagnets

The magnetocaloric effect is studied at the transition to saturation in the antiferromagnetic spin-1/2 Heisenberg model on the simplest two-dimensional lattices, namely the square and the triangular lattice. Numerical results are presented for the entropy which are consistent with identical universal properties. However, the absolute values of the entropy are bigger on the geometrically frustrated triangular lattice than on the non-frustrated square lattice, indicating that frustration improves the magnetocaloric properties.Comment: 2 pages, 2 figures included, to appear in Physica B (proceedings of SCES'05

Critical Properties of the One-Dimensional Forest-Fire Model

The one-dimensional forest-fire model including lightnings is studied numerically and analytically. For the tree correlation function, a new correlation length with critical exponent \nu ~ 5/6 is found by simulations. A Hamiltonian formulation is introduced which enables one to study the stationary state close to the critical point using quantum-mechanical perturbation theory. With this formulation also the structure of the low-lying relaxation spectrum and the critical behaviour of the smallest complex gap are investigated numerically. Finally, it is shown that critical correlation functions can be obtained from a simplified model involving only the total number of trees although such simplified models are unable to reproduce the correct off-critical behaviour.Comment: 24 pages (plain TeX), 4 PostScript figures, uses psfig.st

To Tilt or Not To Tilt: Discrete Gauge Symmetries in Global Intersecting D-Brane Models

Discrete gauge symmetries in global intersecting D-brane models constrain the exact form of the perturbative as well as non-perturbative superpotential. We derive the complete set of conditions on the existence of discrete Zn gauge symmetries on toroidal orbifolds, T6/Z(N) and T6/Z(2)xZ(2M}, with fractional or rigid D6-branes on tilted tori, for which global models of particle physics are known. Several examples of global left-right symmetric and Pati-Salam models are presented. Some discrete `stringy' Zn symmetries are trivial from the field theory point of view, while others have not been identified before.Comment: v2: sections 2.1.1+2.1.2, footnotes 10+11+12, refs added, minor additions+corrections to text, conclusions unchanged; v1: 1+47 page

Discrete Abelian gauge symmetries and axions

We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete Zn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/Z2N and T6/Z2xZ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent Z2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial Z3 charge.Comment: Contribution to the proceedings of DISCRETE2014; 13 page