The many-body radiative heat transfer theory [P. Ben-Abdallah, S.-A. Biehs, and K. Joulain, Phys. Rev. Lett. 107, 114301 (2011)] only considered the contribution from the electric dipole moment. For metal particles, however, the magnetic dipole moment due to eddy current plays an important role, which can further couple with the electric dipole moment to introduce crossed terms. In this work, we develop coupled electric and magnetic dipole (CEMD) approach for the radiative heat transfer in a collection of objects in mutual interaction. Due to the coupled electric and magnetic interactions, four terms, namely the electric-electric, the electric-magnetic, the magnetic-electric and the magnetic-magnetic terms, contribute to the radiative heat flux and the local energy density. The CEMD is applied to study the radiative heat transfer between various dimers of nanoparticles. It is found that each of the four terms can dominate the radiative heat transfer depending on the position and composition of particles. Moreover, near-field many-body interactions are studied by CEMD considering both dielectric and metallic nanoparticles. The near-field radiative heat flux and local energy density can be greatly increased when the particles are in coupled resonances. Surface plasmon polariton and surface phonon polariton can be coupled to enhance the radiative heat flux.
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