New perspectives on the Ising model |
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Authors: | Mancini F |
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Institution: | (1) Dipartimento di Fisica “E.R. Caianiello”, Laboratorio Regionale SuperMat, INFM, Università degli Studi di Salerno, 84081 Baronissi (SA), Italy |
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Abstract: | The Ising model, in presence of an external magnetic field, is
isomorphic to a model of localized interacting particles satisfying
the Fermi statistics. By using this isomorphism, we construct a
general solution of the Ising model which holds for any
dimensionality of the system. The Hamiltonian of the model is solved
in terms of a complete finite set of eigenoperators and eigenvalues.
The Green’s function and the correlation functions of the fermionic
model are exactly known and are expressed in terms of a finite small
number of parameters that have to be self-consistently determined.
By using the equation of the motion method, we derive a set of
equations which connect different spin correlation functions. The
scheme that emerges is that it is possible to describe the Ising
model from a unified point of view where all the properties are
connected to a small number of local parameters, and where the
critical behavior is controlled by the energy scales fixed by the
eigenvalues of the Hamiltonian. By using algebra and symmetry
considerations, we calculate the self-consistent parameters for the
one-dimensional case. All the properties of the system are
calculated and obviously agree with the exact results reported in
the literature. |
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Keywords: | |
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