Curie and Néel temperatures of quantum magnets

We estimate, using high-temperature series expansions, the transition temperatures of the spin 2 , 1 and 3 2 Heisenberg ferromagnet and antiferromagnet in three dimensions. The manner in which the difference between Curie and Néel temperatures vanishes with increasing spin quantum number is investigated. It is well known that in classical spin models, such as the Ising and classical Heisenberg models, on bipartite lattices the critical temperature (if it exists) is the same for ferromagnetic exchange (Curie temperature) as for antiferromagnetic exchange (Néel temperature). This is a direct consequence of the free energy being an even function of the exchange parameter J . It has also been known for some time, but perhaps less widely, that for the quantum spin 1 2 Heisenberg model the Curie and Néel temperatures are unequal. Early work [1, 2] put the Néel temperature some 10% above the Curie temperature for spin 2 , for both the simple cubic (SC) and body centred cubic (BCC) lattices, with the difference decreasing rapidly with increasing S. However, these results were based on rather short series (six terms) and the critical point estimates contained large uncertainties. We have re-investigated this question, using substantially longer series (14th order for S = 2 , 12th order for S = 1, 9th order for S = 3 2 ). This is made possible not only by the massive increase in computing power now available, but also by the development of efficient linked-cluster expansion methods. The reader is referred to a recent review [3] for further details of this method. The Hamiltonian is written in the form H = −J ∑ 〈i j〉 Si · S j − h ∑