Superconducting fluctuations in small grains - the Universal Hamiltonian and the reduced BCS model

Small superconducting grains are discussed in the frameworks of both the reduced BCS Hamiltonian and the Universal Hamiltonian. It is shown that fluctuations of electrons in levels far from the Fermi energy dominate superconducting properties in small and ultrasmall grains. Experimental consequences related to the spin susceptibility and persistent currents of grains and rings with weak electron-electron interactions are discussed.Comment: Contribution to the proceedings of "Fluctuations and phase transitions in superconductors", Nazareth Ilit, Israel, June 10-14, 200

LiHoF4 as a spin-half non-standard quantum Ising system

$\mathrm{LiHoF_{4}}$ is a magnetic material known for its Ising-type anisotropy, making it a model system for studying quantum magnetism. However, the theoretical description of $\mathrm{LiHoF_{4}}$ using the quantum Ising model has shown discrepancies in its phase diagram, particularly in the regime dominated by thermal fluctuations. In this study, we investigate the role of off-diagonal dipolar terms in $\mathrm{LiHoF_{4}}$, previously neglected, in determining its properties. We analytically derive the low-energy effective Hamiltonian of $\mathrm{LiHoF_{4}}$, including the off-diagonal dipolar terms perturbatively, both in the absence and presence of a transverse field. Our results encompass the full $B_{x}-T$ phase diagram, confirming the significance of the off-diagonal dipolar terms in reducing the zero-field critical temperature and determining the critical temperature's dependence on the transverse field. We also highlight the sensitivity of this mechanism to the crystal structure by comparing our calculations with the $\mathrm{Fe_{8}}$ system.Comment: 7+12 pages, 2+4 figure

Ar:N2_2 - a non-universal glass

The bias energies of various two-level systems (TLSs) and their strengths of interactions with the strain are calculated for Ar:N$_2$ glass. Unlike the case in KBr:CN, a distinct class of TLSs having weak interaction with the strain and untypically small bias energies is not found. The addition of CO molecules introduces CO flips which form such a class of weakly interacting TLSs, albeit at much lower coupling than are typically observed in solids. We conclude that because of the absence of a distinct class of weakly interacting TLSs, Ar:N$_2$ is a non-universal glass, the first such system in three dimensions and in ambient pressure. Our results further suggest that Ar:N$_2$:CO may show universal properties, but at temperatures lower than $\approx 0.1$ K, much smaller than typical temperature $\approx 3$ K associated with universality, because of the untypical softness of this system. Our results thus shed light on two long standing questions regarding low temperature properties of glasses: the necessary and sufficient conditions for quantitative universality of phonon attenuation, and what dictates the energy scale of $\approx 3$ K below which universality it typically observed.Comment: 6 pages, 2 figures, results for excitations densities of states are added, presentation improve

Existence of a Thermodynamic Spin-Glass Phase in the Zero-Concentration Limit of Anisotropic Dipolar Systems

The nature of ordering in dilute dipolar interacting systems dates back to the work of Debye and is one of the most basic, oldest and as-of-yet unsettled problems in magnetism. While spin-glass order is readily observed in several RKKY-interacting systems, dipolar spin-glasses are subject of controversy and ongoing scrutiny, e.g., in ${{\rm LiHo_xY_{1-x}F_4}}$, a rare-earth randomly diluted uniaxial (Ising) dipolar system. In particular, it is unclear if the spin-glass phase in these paradigmatic materials persists in the limit of zero concentration or not. We study an effective model of ${{\rm LiHo_xY_{1-x}F_4}}$ using large-scale Monte Carlo simulations that combine parallel tempering with a special cluster algorithm tailored to overcome the numerical difficulties that occur at extreme dilutions. We find a paramagnetic to spin-glass phase transition for all Ho ion concentrations down to the smallest concentration numerically accessible of 0.1%, and including Ho ion concentrations which coincide with those studied experimentally up to 16.7%. Our results suggest that randomly-diluted dipolar Ising systems have a spin-glass phase in the limit of vanishing dipole concentration, with a critical temperature vanishing linearly with concentration, in agreement with mean field theory.Comment: 6 pages, 3 figures, 2 table

Novel disordering mechanism in ferromagnetic systems with competing interactions

Ferromagnetic Ising systems with competing interactions are considered in the presence of a random field. We find that in three space dimensions the ferromagnetic phase is disordered by a random field which is considerably smaller than the typical interaction strength between the spins. This is the result of a novel disordering mechanism triggered by an underlying spin-glass phase. Calculations for the specific case of the long-range dipolar LiHo_xY_{1-x}F_4 compound suggest that the above mechanism is responsible for the peculiar dependence of the critical temperature on the strength of the random field and the broadening of the susceptibility peaks as temperature is decreased, as found in recent experiments by Silevitch et al. [Nature (London) 448, 567 (2007)]. Our results thus emphasize the need to go beyond the standard Imry-Ma argument when studying general random-field systems.Comment: 4+2 pages, 3 figure

Quantum spin glass and the dipolar interaction

Systems in which the dipolar energy dominates the magnetic interaction, and the crystal field generates strong anisotropy favoring the longitudinal interaction terms, are considered. Such systems in external magnetic field are expected to be a good experimental realization of the transverse field Ising model. With random interactions this model yields a spin glass to paramagnet phase transition as function of the transverse field. Here we show that the off-diagonal dipolar interaction, although effectively reduced, destroys the spin glass order at any finite transverse field. Moreover, the resulting correlation length is shown to be small near the crossover to the paramagnetic phase, in agreement with the behavior of the nonlinear susceptibility in the experiments on \LHx. Thus, we argue that the in these experiments a cross-over to the paramagnetic phase, and not quantum criticality, was observed.Comment: To appear in Phys. Rev. Let