Abstract. We reconsider the standard scheme for description of neutrino spin-flavor oscillations aiming at a rigorous derivation of evolution equation for the mixed flavor neutrino states in magnetic field. For this purpose we obtain the evolution equation in the physical basis of massive neutrinos and then trace its transformation into the flavor basis. The effective Hamiltonian of the resulting equation relevant to interaction with the magnetic field differs from the standard one by several entries. The approach leads to interesting relations of the neutrino magnetic moments defined in the two neutrino bases and to some additional subtle properties of the formalism.

In critical systems, the e ect of a localized perturbation a ects points that are arbitrarily far away from the perturbation location. In this paper, we study the e ect of localized perturbations on the solution of the random dimer problem in 2𝐷. By means of an accurate numerical analysis, we show that a local perturbation of the optimal covering induces an excitation whose size is extensive with nite probability. We compute the fractal dimension of the excitations and scaling exponents. In particular, excitations in random dimer problems on non-bipartite lattices have the same statistical properties of domain walls in the 2𝐷 spin glass. Excitations produced in bipartite lattices, instead, are compatible with a loop-erased self-avoiding random walk process. In both cases, we nd evidences of conformal invariance of the excitations, that are compatible with SLE 𝜅 with parameter 𝜅 depending on the bipartiteness of the underlying lattice only.

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