It is the temperature in which the staggered magnetization (= a measure on how much nearest neighbors tend to align oppositely) is nonzero. The magnetization is both zero for a paramagnet and an antiferromagnet.
Can I say for [tex]\sigma=0[/tex], [tex]T=T_N[/tex]?
What do you mean by sigma=0? If you mean that the entropy is zero, I don't think so. It holds when all the local moments are 'fully' aligned(such that two nearest neighbors point in opposite directions). At the Neel temperature, such alignment starts to develop.
Aha! The magnetization! :) In zero fields, the magnetization in the paramagnet-antiferromagnet transition should be always zero. It is not a suitable measure to characterize the transition.