The Lorentz-violating real scalar field at thermal equilibrium A. R. Aguirre, G. Flores-Hidalgo, R. G. Rana and E. S. Souza Eur. Phys. J. C, 81 5 (2021) 459 Published online: 26 May 2021 DOI: 10.1140/epjc/s10052-021-09250-1