6533b7dcfe1ef96bd12733cf

RESEARCH PRODUCT

Thermodynamics of the two-dimensional Heisenberg classical honeycomb lattice

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In this article we adapt a previous work concerning the two-dimensional (2D) Heisenberg classical square lattice [Physica B 245, 263 (1998)] to the case of a honeycomb lattice. Closed-form expressions of the main thermodynamic functions of interest are derived in the zero-field limit. Notably, near absolute zero (i.e., the critical temperature), we derive the values of the critical exponents $\ensuremath{\alpha}=0,\ensuremath{\eta}=\ensuremath{-}1,\ensuremath{\gamma}=3,$ and $\ensuremath{\nu}=1,$ as for the square lattice, thus proving their universal character. A very simple model allows one to give a good description of the low-temperature behaviors of the product $\ensuremath{\chi}T.$ For a 2D-compensated antiferromagnet, we derive simple relations between the characteristics of the maximum of the susceptibility curve $T({\ensuremath{\chi}}_{\mathrm{max}})$ and ${\ensuremath{\chi}}_{\mathrm{max}}$ and the involved exchange energies. Therefore, owing to the knowledge of $T({\ensuremath{\chi}}_{\mathrm{max}})$ and ${\ensuremath{\chi}}_{\mathrm{max}},$ one can directly obtain the respective values of these energies. Finally, we show that the theoretical model allows one to fit correctly experimental susceptibility data of the recently synthetized compound ${\mathrm{Mn}}_{2}{(\mathrm{bpm})(\mathrm{ox})}_{2}{\mathrm{\ensuremath{\cdot}}6\mathrm{H}}_{2}\mathrm{O}$ characterized by a 2D classical honeycomb lattice (where ``bpm'' and ``ox'' are the abbreviations for the ligands bipyrimidine and oxalate, respectively).