The de Almeida–Thouless Line in Hierarchical Quantum Spin Glasses

We determine explicitly and discuss in detail the effects of the joint presence of a longitudinal and a transversal (random) magnetic field on the phases of the Random Energy Model and its hierarchical generalization, the GREM. Our results extent known results both in the classical case of vanishing transversal field and in the quantum case for vanishing longitudinal field. Following Derrida and Gardner, we argue that the longitudinal field has to be implemented hierarchically also in the Quantum GREM. We show that this ensures the shrinking of the spin glass phase in the presence of the magnetic fields as is also expected for the Quantum Sherrington–Kirkpatrick model.

Trimodal-random field Blume-Capel model

The external random magnetic field [Formula: see text] with three nodes, i.e. acting up and down along the [Formula: see text]-axis and zero, effective on the spins in the Blume-Capel model is analyzed on the Bethe lattice in terms of the exact recursion relations. All the nodes are assumed to have the same probability, [Formula: see text], so that the model could give various kinds of phase transitions. As a mapping of the phase transitions, the phase diagrams are constructed on two different planes which present very rich and interesting phase diagrams. In addition to the second- and first-order phase transitions, a few critical points, reentrant and double reentrant behaviors are also observed.

Entanglement and confinement in coupled quantum systems

We study some general properties of coupled quantum systems. We consider simple interactions between two copies of identical Hamiltonians such as the SYK model, Pauli spin chains with random magnetic field and harmonic oscillators. Such couplings make the ground states close to the thermofield double states of the uncoupled Hamiltonians. For the coupled SYK model, we push the numerical computation further towards the thermodynamic limit so that an extrapolation in the size of the system is possible. We find good agreement between the extrapolated numerical result and the analytic result in the large-q limit. We also consider the coupled gauged matrix model and vector model, and argue that the deconfinement is associated with the loss of the entanglement, similarly to the previous observation for the coupled SYK model. The understanding of the microscopic mechanism of the confinement/deconfinement transition enables us to estimate the quantum entanglement precisely, and backs up the dual gravity interpretation which relates the deconfinement to the disappearance of the wormhole. Our results demonstrate the importance of the entanglement between the color degrees of freedom in the emergence of the bulk geometry from quantum field theory via holography.

Loop expansion around the Bethe solution for the random magnetic field Ising ferromagnets at zero temperature

We apply to the random-field Ising model at zero temperature (T=0) the perturbative loop expansion around the Bethe solution. A comparison with the standard ϵ expansion is made, highlighting the key differences that make the expansion around the Bethe solution much more appropriate to correctly describe strongly disordered systems, especially those controlled by a T=0 renormalization group (RG) fixed point. The latter loop expansion produces an effective theory with cubic vertices. We compute the one-loop corrections due to cubic vertices, finding additional terms that are absent in the ϵ expansion. However, these additional terms are subdominant with respect to the standard, supersymmetric ones; therefore, dimensional reduction is still valid at this order of the loop expansion.

Fickian and non-Fickian diffusion of cosmic rays

Fluid approximations to cosmic ray (CR) transport are often preferred to kinetic descriptions in studies of the dynamics of the interstellar medium (ISM) of galaxies, because they allow simpler analytical and numerical treatments. Magnetohydrodynamic simulations of the ISM usually incorporate CR dynamics as an advection–diffusion equation for CR energy density, with anisotropic, magnetic-field-aligned diffusion with the diffusive flux assumed to obey Fick’s law. We compare test particle and fluid simulations of CRs in a random magnetic field. We demonstrate that a non-Fickian prescription of CR diffusion, which corresponds to the telegraph equation for the CR energy density, can be easily calibrated to match the test particle simulations with great accuracy. In particular, we consider a random magnetic field in the fluid simulation that has a lower spatial resolution than that used in the particle simulation to demonstrate that an appropriate choice of the diffusion tensor can account effectively for the unresolved (subgrid) scales of the magnetic field. We show that the characteristic time that appears in the telegraph equation can be physically interpreted as the time required for the particles to reach a diffusive regime and we stress that the Fickian description of the CR fluid is unable to describe complex boundary or initial conditions for the CR energy flux.

Magnetic fields in massive spirals: The role of feedback and initial conditions

Context. Magnetic fields play a very important role in the evolution of galaxies through their direct impact on star formation and stellar feedback-induced turbulence. However, their co-evolution with these processes has still not been thoroughly investigated, and the possible effect of the initial conditions is largely unknown. Aims. This Letter presents the first results from a series of high-resolution numerical models, aimed at deciphering the effect of the initial conditions and of stellar feedback on the evolution of the galactic magnetic field in isolated Milky Way-like galaxies. Methods. The models start with an ordered magnetic field of varying strength, either poloidal or toroidal, and are evolved with and without supernova feedback. They include a dark matter halo, a stellar and a gaseous disk, as well as the appropriate cooling and heating processes for the interstellar medium. Results. Independently of the initial conditions, the galaxies develop a turbulent velocity field and a random magnetic field component in under 15 Myr. Supernova feedback is extremely efficient in building a random magnetic field component up to large galactic heights. However, a random magnetic field emerges even in runs without feedback, which points to an inherent instability of the ordered component. Conclusions. Supernova feedback greatly affects the velocity field of the galaxy up to large galactic heights, and helps restructure the magnetic field up to 10 kpc above the disk, independently of the initial magnetic field morphology. On the other hand, the initial morphology of the magnetic field can accelerate the development of a random component at large heights. These effects have important implications for the study of the magnetic field evolution in galaxy simulations.