Abstract
We introduce a new definition of ordered phase in a magnetic system based on properties of the local spin state probability. A statistical functional associated to this quantity depends both on amplitude and direction of the local magnetization. We show that it is possible to introduce an expansion at fixed magnetization amplitude in the inverse of lattice coordination number if the direction is selected by an extremum condition. In the limit of infinite coordination number we recover the mean field results. First order corrections are derived for the Ising model in the presence of a transverse field and for the XY model. Our results concerning critical temperature and order parameter compare favorably with other approaches.
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de Pasquale, F., Giampaolo, S.M. Expansion Around the Mean Field in Quantum Magnetic Systems. Journal of Statistical Physics 115, 125–142 (2004). https://doi.org/10.1023/B:JOSS.0000019837.56894.8a
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DOI: https://doi.org/10.1023/B:JOSS.0000019837.56894.8a