Spin Glasses

This is a short review about recent methods and results, mostly for mean field spin glasses, based on interpolation and comparison schemes. In particular, the Parisi spontaneous replica symmetry breaking phenomenon is described in the frame of extended variational principles, Derrida-Ruelle probability cascades, and overlap locking.Comment: 25 page

SOME ASPECTS OF CHARGE STATIC FIELD POTENTIAL IN THREE- DIMENSIONAL ELECTRODYNAMICS

Obtaining the expicit expression for a point charge field potential in three-dimensional electrodynamics when the vacuum polarization is taken into account; comparison of the results obtained by the different methods of calculation. The present work is a continuation of Ref. [1]. It is of interest from the point of view of further studying the chiral symmetry dynamic breaking in QED 3 [2-11] and the properties of planar structures in solid physics [12-15]

Symmetry effects on the static and dynamic properties of coupled magnetic oscillators

The effect of symmetry on the resonance spectra of antiferromagnetically coupled oscillators has attracted new interest with the discovery of symmetry-breaking induced anti-crossings. Here, we experimentally characterise the resonance spectrum of a synthetic antiferromagnet Pt/CoFeB/Ru/CoFeB/Pt, where we are able to independently tune the effective magnetisation of the two coupled magnets. To model our results we apply the mathematical methods of group theory to the solutions of the Landau Lifshitz Gilbert equation. This general approach, usually applied to quantum mechanical systems, allows us to identify the main features of the resonance spectrum in terms of symmetry breaking and to make a direct comparison with crystal antiferromagnets

Casimir Forces at Tricritical Points: Theory and Possible Experiments

Using field-theoretical methods and exploiting conformal invariance, we study Casimir forces at tricritical points exerted by long-range fluctuations of the order-parameter field. Special attention is paid to the situation where the symmetry is broken by the boundary conditions (extraordinary transition). Besides the parallel-plate configuration, we also discuss the geometries of two separate spheres and a single sphere near a planar wall, which may serve as a model for colloidal particles immersed in a fluid. In the concrete case of ternary mixtures a quantitative comparison with critical Casimir and van der Waals forces shows that, especially with symmetry-breaking boundaries, the tricritical Casimir force is considerably stronger than the critical one and dominates also the competing van der Waals force.Comment: 18 pages, Latex, 3 postscript figures, uses Elsevier style file

Valence Bond States: Link models

An isotropic anti-ferromagnetic quantum state on a square lattice is characterized by symmetry arguments only. By construction, this quantum state is the result of an underlying valence bond structure without breaking any symmetry in the lattice or spin spaces. A detailed analysis of the correlations of the quantum state is given (using a mapping to a 2D classical statistical model and methods in field theory like mapping to the non-linear sigma model or bosonization techniques) as well as the results of numerical treatments (regarding exact diagonalization and variational methods). Finally, the physical relevance of the model is motivated. A comparison of the model to known anti-ferromagnetic Mott-Hubbard insulators is given by means of the two-point equal-time correlation function obtained i) numerically from the suggested state and ii) experimentally from neutron scattering on cuprates in the anti-ferromagnetic insulator phase.Comment: 20 pages, 15 figures; added references, corrected some typos, new sections. Published versio

Symmetry and symmetry breaking in coupled oscillator communities [post-print]

With the recent development of analytical methods for studying the collective dynamics of coupled oscillator systems, the dynamics of communities of coupled oscillators have received a great deal of attention in the nonlinear dynamics community. However, the majority of these works treat systems with a number of symmetries to simplify the analysis. In this work we study the role of symmetry and symmetry-breaking in the collective dynamics of coupled oscillator communities, allowing for a comparison between the macroscopic dynamics of symmetric and asymmetric systems. We begin by treating the symmetric case, deriving the bifurcation diagram as a function of intra- and intercommunity coupling strengths. In particular we describe transitions between incoherence, standing wave, and partially synchronized states and reveal bistability regions. When we turn our attention to the asymmetric case we find that the symmetry-breaking complicates the bifurcation diagram. For instance, a pitchfork bifurcation in the symmetric case is broken, giving rise to a Hopf bifurcation. Moreover, an additional partially synchronized state emerges, as well as a new bistability region