Abstract
We consider the statistical mechanics of a layered superconductor in a magnetic field. The superconductor is described as a periodic system of superconducting layers coupled via a magnetic field. Each layer contains a gas of two-dimensional pancakes and antipancakes. To obtain the free energy of the pancake gas we used the method of collective variables which gives not only the main results of the Debye-H\uckel theory, but corrections to it as well. We have calculated the magnetization which shows all the main features of the reversible magnetization of high-temperature superconductors.
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