for | E | < N J log ⁡ ⁡ 2 . However this expression only holds if the entropy per spin, lim N → → ∞ ∞ S ( E ) / N is finite, i.e., when | E | < − − N J log ⁡ ⁡ 2 . Since ( 1 / T ) = ∂ ∂ S / ∂ ∂ E , this corresponds to T > T c = 1 / ( 2 log ⁡ ⁡ 2 ) . For T < T c , the system remains "frozen" in a small number of configurations of energy E ≃ ≃ − − N J log ⁡ ⁡ 2 and the entropy per spin vanishes in the thermodynamic limit.