Related papers: One-loop topological expansion for spin glasses in…
The Lieb-Schultz-Mattis theorem and its higher dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy…
By means of parallel tempering Monte Carlo simulations we find strong evidence for a finite-temperature spin-glass transition in a system of diluted classical Heisenberg dipoles randomly placed on the sites of a simple cubic lattice. We…
Interacting bosons in optical lattices directly expose quantum phases in a clean, highly controllable environment. This requires engineering systems with very low entropies, but the resulting temperature--interaction ratios $T/U$ of present…
Bethe Lattice Spin Glasses (BLSG) are models with finite connectivity which undergo a Replica Symmetry Breaking (RSB) phase transition in field, even at zero temperature. The order parameter describing this phase is a function related to…
We develop a resummed high-temperature expansion for lattice spin systems with long range interactions, in models where the free energy is not, in general, analytic. We establish uniqueness of the Gibbs state and exponential decay of the…
We discuss a phase transition in spin glass models which have been rarely considered in the past, namely the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e. at a smaller overlap) than…
We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function $q(x)$ is computed at high orders in powers of $\tau=T_c-T$ and $H$. We find that none of…
We study fully occupied lattice systems of classical magnetic dipoles which point along random axes. Only dipolar interactions are considered. From tempered Monte Carlo simulations, we obtain numerical evidence that supports the following…
The average ground state energy and entropy for +/- J spin glasses on Bethe lattices of connectivities k+1=3...,26 at T=0 are approximated numerically. To obtain sufficient accuracy for large system sizes (up to n=2048), the Extremal…
We investigate spin-1/2 electrons with local Hubbard interaction and variable range hopping amplitudes which decay like~$\sinh(\kappa)/\sinh(\kappa r)$. Assuming integrability the Asymptotic Bethe Ansatz approach allows us to derive the…
Linked cluster expansions provide a useful tool for both analytical and numerical investigations of lattice field theories. The expansion parameter(s) being the interaction strength(s) fields at neighboured lattice sites are coupled, they…
A family of spin-lattice models are derived as convergent finite dimensional approximations to the rest frame kinetic energy of a barotropic fluid coupled to a massive rotating sphere. In not fixing the angular momentum of the fluid…
The average ground state energies for spin glasses on Bethe lattices of connectivities r=3,...,15 are studied numerically for a Gaussian bond distribution. The Extremal Optimization heuristic is employed which provides high-quality…
Despite the extreme simplicity in their definition, spin glasses disclose a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis we try to shed light on some of them, focusing on one hand on the search of…
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian…
We report on a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisenberg chain we derive, for arbitrary values of the anysotropy, a single non-linear…
The goal of this chapter is to review recent analytical results about the growth of a (static) correlation length in glassy systems, and the connection that can be made between this length scale and the equilibrium correlation time of its…
We study the effects of random pinning on the Fredrickson-Andersen model on the Bethe lattice. We find that the nonergodic transition temperature rises as the fraction of the pinned spins increases and the transition line terminates at a…
The interplay between topology, dissipation and nonlinearities can give rise to a wealth of new phenomena and pave the way for novel topological lasers, sensors and other quantum devices. Along these lines, we propose here an optomechanical…
We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica…