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arXiv · 1510.07341

Microscopic theory of phase transitions in a critical region

Vitaly V. Kocharovsky·Vladimir V. Kocharovsky
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Abstract

The problem of finding a microscopic theory of phase transitions across a critical point is a central unsolved problem in theoretical physics. We find a general solution to that problem and present it here for the cases of Bose-Einstein condensation in an interacting gas and ferromagnetism in a lattice of spins, interacting via a Heisenberg or Ising Hamiltonian. For Bose-Einstein condensation, we present the exact, valid for the entire critical region, equations for the Green functions and order parameter, that is a critical-region extension of the Beliaev-Popov and Gross-Pitaevskii equations. For the magnetic phase transition, we find an exact theory in terms of constrained bosons in a lattice and obtain similar equations for the Green functions and order parameter. In particular, we outline an exact solution for the three-dimensional Ising model.

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Vitaly V. Kocharovsky, Vladimir V. Kocharovsky. 2016-01-01. Microscopic theory of phase transitions in a critical region. https://doi.org/10.1088/0031-8949%2F90%2F10%2F108002

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