Using the numerical approach for a study of the thermodynamic properties of the nonuniform one–dimensional spin- 1 2 isotropic XY model in a transverse field we examine different lattice distortions to reveal which spin–Peierls phases are realized in the magnetic chain at zero temperature in the presence of external field. An interest in the theoretical study of quantum spin chains exhibiting spin–Peierls phases has incredibly grown since the discovery of the first inorganic spin–Peierls compound CuGeO3 (for a review see 1). Although the quantum Heisenberg model is usually used as an appropriate model to describe the spin–Peierls phase transition in the available materials some generic features can be clarified within the framework of the simpler spin- 1 2 isotropic XY chain (see2,3 and references therein). The latter spin model can be reformulated using the Jordan–Wigner transformation as a one–dimensional model of tight–binding spinless fermions. As a result, the exhaustive analytical and numerical analysis of different properties of the model becomes possible. In what follows we analyze a stability of various spin–Peierls phases at zero temperature in the presence of external field. For this purpose we consider a nonuniform spin- 1 2 chain in a transverse field defined by the Hamiltonia
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