Replica-symmetric solutions of a dilute Ising ferromagnet in a random field

We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the replica-symmetric context, the problem is reduced to the analysis of the solutions of a nonlinear integral equation. At zero temperature, and under some restrictions on the form of the random fields, we are able to perform a detailed analysis of stability of the replica-symmetric solutions. In contrast to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a uniform field, the paramagnetic solution is fully stable in a sufficiently large random field

Three-dimensional Dirac oscillator in a thermal bath

The thermal properties of the three-dimensional Dirac oscillator are considered. The canonical partition function is determined, and the high-temperature limit is assessed. The degeneracy of energy levels and their physical implications on the main thermodynamic functions are analyzed, revealing that these functions assume values greater than the one-dimensional case. So that at high temperatures, the limit value of the specific heat is three times bigger.Comment: 9 pages, 4 figures. Text improved, references added. Revised to match accepted version in Europhysics Letters

Uniform approximation for the overlap caustic of a quantum state with its translations

The semiclassical Wigner function for a Bohr-quantized energy eigenstate is known to have a caustic along the corresponding classical closed phase space curve in the case of a single degree of freedom. Its Fourier transform, the semiclassical chord function, also has a caustic along the conjugate curve defined as the locus of diameters, i.e. the maximal chords of the original curve. If the latter is convex, so is its conjugate, resulting in a simple fold caustic. The uniform approximation through this caustic, that is here derived, describes the transition undergone by the overlap of the state with its translation, from an oscillatory regime for small chords, to evanescent overlaps, rising to a maximum near the caustic. The diameter-caustic for the Wigner function is also treated.Comment: 14 pages, 9 figure

Physical properties of the Schur complement of local covariance matrices

General properties of global covariance matrices representing bipartite Gaussian states can be decomposed into properties of local covariance matrices and their Schur complements. We demonstrate that given a bipartite Gaussian state $\rho_{12}$ described by a $4\times 4$ covariance matrix \textbf{V}, the Schur complement of a local covariance submatrix $\textbf{V}_1$ of it can be interpreted as a new covariance matrix representing a Gaussian operator of party 1 conditioned to local parity measurements on party 2. The connection with a partial parity measurement over a bipartite quantum state and the determination of the reduced Wigner function is given and an operational process of parity measurement is developed. Generalization of this procedure to a $n$-partite Gaussian state is given and it is demonstrated that the $n-1$ system state conditioned to a partial parity projection is given by a covariance matrix such as its $2 \times 2$ block elements are Schur complements of special local matrices.Comment: 10 pages. Replaced with final published versio