Gravity in 2+1 dimensions as a Riemann-Hilbert problem

In this paper we consider 2+1-dimensional gravity coupled to N point-particles. We introduce a gauge in which the $z$- and $\bar{z}$-components of the dreibein field become holomorphic and anti-holomorphic respectively. As a result we can restrict ourselves to the complex plane. Next we show that solving the dreibein-field: $e^a_z(z)$ is equivalent to solving the Riemann-Hilbert problem for the group $SO(2,1)$. We give the explicit solution for 2 particles in terms of hypergeometric functions. In the N-particle case we give a representation in terms of conformal field theory. The dreibeins are expressed as correlators of 2 free fermion fields and twistoperators at the position of the particles.Comment: 32 pages Latex, 4 figures (uuencoded

Tunnelling series in terms of perturbation theory for quantum spin systems

Considered is quantum tunnelling in anisotropic spin systems in a magnetic field perpendicular to the anisotropy axis. In the domain of small field the problem of calculating tunnelling splitting of energy levels is reduced to constructing the perturbatio n series with degeneracy, the order of degeneracy being proportional to a spin value. Partial summation of this series taking into account ''dangerous terms'' with small denominators is performed and the value of tunnelling splitting is calculated with allowance for the first correction with respect to a magnetic field.Comment: 7 pages, REVTeX 3.

Quantum statistical metastability for a finite spin

We study quantum-classical escape-rate transitions for uniaxial and biaxial models with finite spins S=10 (such as Mn_12Ac and Fe_8) and S=100 by a direct numerical approach. At second-order transitions the level making a dominant contribution into thermally assisted tunneling changes gradually with temperature whereas at first-order transitions a group of levels is skipped. For finite spins, the quasiclassical boundaries between first- and second-order transitions are shifted, favoring a second-order transition: For Fe_8 in zero field the transition should be first order according to a theory with S \to \infty, but we show that there are no skipped levels at the transition. Applying a field along the hard axis in Fe_8 makes transition the strongest first order. For the same model with S=100 we confirmed the existence of a region where a second-order transition is followed by a first-order transition [X. Martines Hidalgo and E. M. Chudnovsky, J. Phys.: Condensed Matter (in press)].Comment: 7 Phys. Rev. pages, 10 figures, submitted to PR

Dipolar ordering in Fe8?

We show that the low-temperature physics of molecular nanomagnets, contrary to the prevailing one-molecule picture, must be determined by the long-range magnetic ordering due to many-body dipolar interactions. The calculations here performed, using Ewald's summation, suggest a ferromagnetic ground state with a Curie temperature of about 130 mK. The energy of this state is quite close to those of an antiferromagnetic state and to a glass of frozen spin chains. The latter may be realized at finite temperature due to its high entropy.Comment: 7 pages, no figures, submitted to EP

Magnetization of nanoparticle systems in a rotating magnetic field

The investigation of a sizable thermal enhancement of magnetization is put forward for uniaxial ferromagnetic nanoparticles that are placed in a rotating magnetic field. We elucidate the nature of this phenomenon and evaluate the resonant frequency dependence of the induced magnetization. Moreover, we reveal the role of magnetic dipolar interactions, point out potential applications and reason the feasibility of an experimental observation of this effect.Comment: 10 pages, 2 figure

Macroscopic Quantum Coherence in a Magnetic Nanoparticle Above the Surface of a Superconductor

We study macroscopic quantum tunneling of the magnetic moment in a single-domain particle placed above the surface of a superconductor. Such a setup allows one to manipulate the height of the energy barrier, preserving the degeneracy of the ground state. The tunneling amplitude and the effect of the dissipation in the superconductor are computed.Comment: RevTeX, 4 pages, 1 figure. Submitted to Phys. Rev. Let

First- and second-order transitions of the escape rate in ferrimagnetic or antiferromagnetic particles

Quantum-classical escape-rate transition has been studied for two general forms of magnetic anisotropy in ferrimagnetic or antiferromagnetic particles. It is found that the range of the first-order transition is greatly reduced as the system becomes ferrimagnetic and there is no first-order transition in almost compensated antiferromagnetic particles. These features can be tested experimentally in nanomagnets like molecular magnets.Comment: 11 pages, 3 figures, to appear in Europhys. Let

Macroscopic Quantum Tunneling and Dissipation of Domain Wall in Ferromagnetic Metals

The depinning of a domain wall in ferromagentic metal via macroscopic quantum tunneling is studied based on the Hubbard model. The dynamics of the magnetization verctor is shown to be governed by an effective action of Heisenberg model with a term non-local in time that describes the dissipation due to the conduction electron. Due to the existence of the Fermi surface there exists Ohmic dissipation even at zero temperature, which is crucially different from the case of the insulator. Taking into account the effect of pinning and the external magnetic field the action is rewritten in terms of a collective coordinate, the position of the wall, $Q$. The tunneling rate for $Q$ is calculated by use of the instanton method. It is found that the reduction of the tunneling rate due to the dissipation is very large for a thin domain wall with thickness of a few times the lattice spacing, but is negligible for a thick domain wall. Dissipation due to eddy current is shown to be negligible for a wall of mesoscopic size.Comment: of pages 26, to appear in "Quantum Tunneling of Magnetization, ed. B. Barbara and L. Gunther (Kluwer Academic Pub.), Figures available by FAX (81-48-462-4649