Weak-coupling phenomena of the two-dimensional Hubbard model is gaining momentum as a new interesting research field due to its extraordinarily rich behavior as a function of the carrier density and model parameters. Salmhofer (1998 Commun. Math. Phys. 194 249; 2001 Phys. Rev. Lett. 87 187004) developed a new renormalization-group method for interacting Fermi systems and Metzner (2000 Phys. Rev. B 61 7364; 2000 Phys. Rev. Lett. 85 5162) implemented this renormalization group analysis of the two-dimensional Hubbard model. In this work, we demonstrate the spin-wave dependent electronic structure and susceptibility behavior of model graphene–phosphorene van der Waals heterostructure in the framework of renormalization group approach. We implement singlet vertex response function for the weakly interacting van der Waals Fermi system with nearest-neighbor hopping amplitudes. This analytical approach is further extended for spin-wave dependent susceptibility behavior. We present the resulting compressibility and phase diagram in the vicinity of half-filling, and also results for the density dependence of the critical energy scale.

A three‐orbital per site theoretical model study is attempted to analyze the nature of specific heat in iron‐based superconductors. Based on recent experimental data, it is found that the five Fe 3d orbitals, Hund's coupling, and intra‐ and inter‐electron orbital correlations play a significant role in the electronic properties of these systems. Thus, in the present work, a model Hamiltonian containing hopping between orbitals, Hund's coupling, and intra‐ and inter‐orbital Coulomb interactions is employed for iron pnictide. Employing Green's function technique within Bardeen–Cooper–Schrieffer (BCS) mean‐field approximation, expressions of superconducting energy gap parameter and quasiparticle energies are obtained. Considering these parameters, specific heat is calculated and its variation with temperature and other parameters of the model Hamiltonian is analyzed. Also, a pseudogap (PG) parameter, arising out of multi‐orbitals’ Hund's coupling, as supported by angle‐resolved photoemission spectroscopy and scanning tunneling microscopy experiments, is introduced. The expression of specific heat is numerically analyzed to pinpoint its variation below and above the transition temperature (T c). Self‐consistent numerical analysis of the specific heat jump as a function of multi‐orbital hopping, electron interactions, and Hund's coupling in terms of PG parameter is shown in detail. Finally, the outcomes are compared with recent theoretical and experimental data available on specific heat variations in iron superconductors like LaOFeAs system.