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.

References in corpus (3)

• The Hubbard model within the equations of motion approach
• Fermionic systems with charge correlations
• New perspectives on the Ising model

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• One-dimensional extended Hubbard model in the atomic limit
• Composite Operator Method analysis of the underdoped cuprates puzzle
• Equations of motion approach to the spin-1/2 Ising model on the Bethe lattice
• 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