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The determination of the Landau free energy (the grand thermodynamic potential) by a perturbation theory is advanced to arbitrary order for the specific case of non-interacting fermionic systems perturbed by a one-particle potential. Peculiar features of the formalism are highlighted, and its applicability for bosons is indicated. The results are employed to develop a more explicit approach describing exchange interactions between spins of Andersons magnetic impurities in metals, semiconductors, and insulators. Within the fourth order our theory provides on the equal footing formulae for the Ruderman-Kittel-Kasuya-Yosida, Bloembergen-Rowland, superexchange, and two-electron exchange integrals at non-zero temperature.
The existence or absence of non-analytic cusps in the Loschmidt-echo return rate is traditionally employed to distinguish between a regular dynamical phase (regular cusps) and a trivial phase (no cusps) in quantum spin chains after a global quench. H
For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several truncations of the
We study magnetic fluctuations in a system of interacting spins on a lattice at high temperatures and in the presence of a spatially varying magnetic field. Starting from a microscopic Hamiltonian we derive effective equations of motion for the spins
In recent years significant attention has been attracted to proposals which utilize DNA for nanotechnological applications. Potential applications of these ideas range from the programmable self-assembly of colloidal crystals, to biosensors and nanop
A mean-field approach (MFA) is proposed for the analysis of orientational order in a two-dimensional system of stochastic self-propelled particles interacting by local velocity alignment mechanism. The treatment is applied to the cases of ferromagnet