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

Abstract

The rigorously solvable (quadratic in Fermi creation and annihilation opreators) part of the Hamiltonian of the 1D Ising model ( S = $) 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 a t two longrange interaction laws. The spectrum has some peculiarities; the energy gap vanishes only in the centre of the zone at H = H,, which leads t o 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. PaccMoTpeHa Tom0 peruaeMaR (KBanpaTHsHaR no cDepMH onepaTopaM pomneamzr