One‐dimensional ising model with an infinite radius of interaction in a transverse magnetic field. Some thermodynamic properties of the rigorously solvable part

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.