Exact solution of the one-dimensional spin-$\frac{3}{2}$ Ising model in magnetic field

Abstract

In this paper, we study the Ising model with general spin $S$ in presence of an external magnetic field by means of the equations of motion method and of the Green's function formalism. First, the model is shown to be isomorphic to a fermionic one constituted of $2S$ species of localized particles interacting via an intersite Coulomb interaction. Then, an exact solution is found, for any dimension, in terms of a finite, complete set of eigenoperators of the latter Hamiltonian and of the corresponding eigenenergies. This explicit knowledge makes possible writing exact expressions for the corresponding Green's function and correlation functions, which turn out to depend on a finite set of parameters to be self-consistently determined. Finally, we present an original procedure, based on algebraic constraints, to exactly fix these latter parameters in the case of dimension 1 and spin $\frac{3}{2}$. For this latter case and, just for comparison, for the cases of dimension 1 and spin $\frac{1}{2}$ [F. Mancini, Eur. Phys. J. B \textbf{45}, 497 (2005)] and spin 1 [F. Mancini, Eur. Phys. J. B \textbf{47}, 527 (2005)], relevant properties such as magnetization $<S>$ and square magnetic moment $<S^2>$, susceptibility and specific heat are reported as functions of temperature and external magnetic field both for ferromagnetic and antiferromagnetic couplings. It is worth noticing the use we made of composite operators describing occupation transitions among the 3 species of localized particles and the related study of single, double and triple occupancy per site.

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• Equations of motion approach to the spin-1/2 Ising model on the Bethe lattice
• Exact solution of the 1D Hubbard model in the atomic limit with inter-site magnetic coupling
• Different orderings in the narrow-band limit of the extended Hubbard model on the Bethe lattice
• The composite operator method route to the 2D Hubbard model and the cuprates
• The high-temperature expansion of the classical Ising model with S_z^2 term
• COM(3p) solution of the 2D Hubbard model: momentum resolved quantities
• Fermionic systems with charge correlations on the Bethe lattice
• A class of solvable models in Condensed Matter Physics