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arXiv:1202.2237 · Journal of Statistical Mechanics Theory and Experiment

Correlation equalities and upper bounds for the transverse Ising model

F C Sá Barreto, A L Mota

Published May 11, 2012• 8 citations
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Abstract

Starting from an exact formal identity for the two-state transverse Ising model and using correlation inequalities, approximate upper bounds for the critical temperature and the critical transverse field are obtained, which improve the effective results.
DOI
10.1088/1742-5468/2012/05/p05006

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A new type effective field approach is used to derive the thermodynamical properties of the transverse Ising model. The method is based on an exact formal identity for the two-state transverse Ising model and utilizes an exponential operator technique. The lines of critical points in the Ω-T plane are derived and the critical transverse fields ΩC are obtained analytically, for lattices with coordination numbers z = 2, 4 and 6. This simple method yields results which represent a remarkable improvement on the usual mean field approximation. Our results are also compared with those from series expansion method.
The Ising model with a transverse field has been investigated for both positive and negative exchange interactions. Effective Hamiltonians are used for a pair of nearest-neighbour spins. The transition temperature and susceptibility above the transition temperature are calculated. The critical magnitude of the transverse field for which the transition temperature becomes 0 K is also evaluated. When the transverse field is absent, the result of the present method is reduced to that of the Bethe approximation.