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Within the framework of effective Lagrangians we calculate the free energy density for an O($N$) antiferromagnet in 2+1 dimensions up to three-loop order in the perturbative expansion and derive the low-temperature series for various thermodynamic quantities.
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Note also, that this counting scheme only applies within a Lorentz-invariant framework: Loop corrections involving ferromagnetic magnons, e.g., which follow a quadratic dispersion relation, are suppressed by three powers of momentum in four space-time dimensions and suppressed by two powers of momentum in three space-time dimensions
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For a review of the effective Lagrangian method at non-zero temperature, see refs. [ 21 ] . For a general review of field theory at finite temperature, see refs. [ 22 ]
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