Abstract
In this paper we present calculations of the SO(5) quantum rotor theory of high-${T}_{c}$ superconductivity in a Zeeman magnetic field. We use the spherical approach for five-component quantum rotors in a three-dimensional lattice to obtain formulas for the critical lines, free energy, entropy, specific heat, and present temperature dependences of these quantities for different values of the magnetic field. Our results are in qualitative agreement with relevant experiments on high-${T}_{c}$ cuprates.
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