Beta Decay in Medium-Mass Nuclei with the In-Medium Similarity Renormalization Group

We review the status of ab initio calculations of allowed beta decays (both Fermi and Gamow–Teller), within the framework of the valence-space in-medium similarity renormalization group approach.

The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation

We investigate the thermodynamic uncertainty relation for the $$(1+1)$$ ( 1 + 1 ) dimensional Kardar–Parisi–Zhang (KPZ) equation on a finite spatial interval. In particular, we extend the results for small coupling strengths obtained previously to large values of the coupling parameter. It will be shown that, due to the scaling behavior of the KPZ equation, the thermodynamic uncertainty relation (TUR) product displays two distinct regimes which are separated by a critical value of an effective coupling parameter. The asymptotic behavior below and above the critical threshold is explored analytically. For small coupling, we determine this product perturbatively including the fourth order; for strong coupling we employ a dynamical renormalization group approach. Whereas the TUR product approaches a value of 5 in the weak coupling limit, it asymptotically displays a linear increase with the coupling parameter for strong couplings. The analytical results are then compared to direct numerical simulations of the KPZ equation showing convincing agreement.

The mixed spin-3/2 and spin-2 Blume-Capel model by renormalization group approach

PurposeThe authors investigate the magnetic properties of a mixed spin-3/2 and spin-2 Blume-Capel model on square and cubic lattices with two different single-ion anisotropies.Design/methodology/approachTo study the critical behavior of a mixed spin-3/2 and spin-2 system, the authors have used a real space renormalization group approximation and specifically the Migdal-Kadanoff technique. The authors give the phase diagrams for two different cases: (1) on the (Δ/|J|, 1/|J|) plane with ΔA = ΔB = Δ, and (2) on the (ΔA/|J|, 1/|J|) and (ΔB/|J|, 1/|J|) planes for selected values of ΔB/|J| and ΔA/|J|, respectively.FindingsThe phase diagrams obtained show that the system exhibits both second- and first-order phase transitions as well as tricritical points for some values of the anisotropies. Moreover, using the variation of the free energy and its derivative at low temperatures, the authors have seen the appearance of first-order transitions at very low temperatures.Originality/valueFew investigations of mixed spin-3/2 and spin-2 systems with crystal field have been realized. For this reason, the authors use the renormalization group approach to complete the work done on these systems. In absence of an exact solution, this contributes to the synthesis of the approximation results on mixed spins models.