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One‐dimensional ising model with an infinite radius of interaction in a transverse magnetic field. Some thermodynamic properties of the rigorously solvable part
Author(s) -
Georgiev G. I.,
Sandalski M. P.
Publication year - 1979
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220940218
Subject(s) - hamiltonian (control theory) , physics , ising model , quadratic equation , gravitational singularity , condensed matter physics , phase transition , transversal (combinatorics) , coupling constant , magnetic field , mathematical physics , quantum mechanics , mathematics , mathematical analysis , geometry , mathematical optimization
The rigorously solvable (quadratic in Fermi creation and annihilation opreators) part of the Hamiltonian of the ID Ising model ( S = 1/2) with an infinite radius of interaction is studied in a transversal magnetic field H . After diagonalization of the Hamiltonian, an analytical and numerical investigation is made for the spectrum and some basic thermodynamic quantities at two long‐range interaction laws. The spectrum has some peculiarities; the energy gap vanishes only in the centre of the zone at H = H / cr which leads to singularities in some quantities and is reflected in the phase transition in the model considered. Some dependences of the thermodynamic quantities on H and on the coupling constants are obtained from the numerical data.