Criticality of the Mean-Field Spin-Boson Model: Boson State Truncation and Its Scaling Analysis

The spin-boson model has nontrivial quantum phase transitions at zero temperature induced by the spin-boson coupling. The bosonic numerical renormalization group (BNRG) study of the critical exponents $\beta$ and $\delta$ of this model is hampered by the effects of boson Hilbert space truncation. Here we analyze the mean-field spin boson model to figure out the scaling behavior of magnetization under the cutoff of boson states $N_{b}$. We find that the truncation is a strong relevant operator with respect to the Gaussian fixed point in $0<s<1/2$ and incurs the deviation of the exponents from the classical values. The magnetization at zero bias near the critical point is described by a generalized homogeneous function (GHF) of two variables $\tau=\alpha-\alpha_{c}$ and $x=1/N_{b}$. The universal function has a double-power form and the powers are obtained analytically as well as numerically. Similarly, $m(\alpha=\alpha_{c})$ is found to be a GHF of $\epsilon$ and $x$. In the regime $s>1/2$, the truncation produces no effect. Implications of these findings to the BNRG study are discussed.Comment: 9 pages, 7 figure

Influences on the triple alpha process beyond the Hoyle state

The triple alpha process is studied using indirect methods. The beta decays of 12N and 12B are used to probe the triple alpha continuum of 12C. Different independent breakup channels are identified, consistently showing that the 10 MeV strength is dominated by a 0+ state interfering with the Hoyle state ghost. The 13.14 MeV region on the other hand is dominated by a 2+ state. Present: National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan MI-48824, USA.</p

A new three-parameter H, G₁, G₂ magnitude phase function for asteroids

International audienceWe have developed a new three-parameter H, G1, G2 magnitude phase function for asteroids. The phase function is aimed at replacing the currently adopted two-parameter H, G phase function. We show that H, G1, G2 produces better fits of available magnitude - phase curves of well-observed asteroids. We show also that the new system can be conveniently reduced to a two-parameter H, G12 magnitude phase function, which allows us to derive better estimates of the absolute magnitudes of asteroids for which poorly-sampled magnitude phase curves are available