The thermodynamics of the unitary (normalized spin) quantum and classical Ising models with skew magnetic field, for |J|β≲0.9, is derived for the ferromagnetic and antiferromagnetic cases. The high-temperature expansion (β-expansion) of the Helmholtz free energy is calculated up to order β7...

The β-expansion of the Helmholtz free energy (HFE) up to order β12 of the classical XYZ model with a single-ion anisotropy term and external magnetic field is calculated and compared to the numerical solution of Joyce's [Phys. Rev. Lett. 19 (1967) 581] for the XXZ classical model, with neither...

In a recent work (J. Math. Phys. 43 (2002) 1390) we derived analytical expressions for the coefficients in the high temperature expansion of the Helmholtz free energy of periodic one-dimensional chains in the cumulant method, for arbitrary order in β. In order to do so, an auxiliary function...

We study the thermal properties of the quantum and classical models of the Fe4 and Fe8 SMMs in the presence of an arbitrary constant magnetic field, obtaining the β-expansions of the Helmholtz free energy of the models up to orders β26, β25 and β26 for the spin-5 (Fe4), the spin-10 (Fe8) and...

We revisit the method of calculating the β-expansion of the Helmholtz free energy of any one-dimensional (1D) Hamiltonian with invariance under space translations, presented in [O. Rojas, S.M. de Souza, M.T. Thomaz, J. Math. Phys. 43 (2002) 1390], extending this method to 1-D Hamiltonians that...

We explore the properties of the non-commutative Grassmann algebra to study the unidimensional Generalized Hubbard model, obtaining the analytical expressions for the first three terms in the high temperature expansion of its grand canonical partition function, with no restrictions to the...

We explore the properties of the non-commutative Grassmann algebra to obtain the high-temperature expansion of the grand canonical partition function for self-interacting fermionic systems. As an application, we consider the anharmonic fermionic oscillator, the simplest model in Quantum...

Geometrically frustrated spin models with competing interaction parameters and the phase diagram of their corresponding T=0 ground state energies are studied. The partition function defined by means of the transfer matrix method is calculated and the thermodynamical properties of the diamond...

The paper discusses the transformation of decorated Ising models into an effective undecorated spin model, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes [−s,s] is...

Thermodynamical properties of spin-S Ising chains can nowadays be easily obtained using numerical calculation. However, from a mathematical point of view, its exact solution for arbitrary spin is still a challenge. Only limiting cases have been solved exactly, such as the infinite spin limit and...