We apply the cummulant method to obtain the high-temperature expansion of the Helmholtz free energy of the tetrahedral spin-1/2 and spin-2 XXZ models. The tetrahedral model is written as a composite spin-1 XXZ model, and some of its thermodynamic functions are compared to those of the ordinary spin-1 XXZ model. The composite spin-1 model is then mapped onto a fermion model, and it is shown that the contribution of the string Hamiltonian to thermodynamic functions at high temperatures cannot be neglected. The hightemperature expansion of the Helmholtz free energy of the anisotropic spin-2 XXZ chain is obtained up to order ␤ 6 . Our results fit well the numerical quantum Monte Carlo data calculated by Yamamoto ͓Phys. Rev. B 53, 3364 ͑1996͔͒ for the isotropic antiferromagnetic Heisenberg chain. We complement his high-temperature expansions for thermodynamic functions with terms of higher order in ␤.

We analyze the electromagnetic response of a system of charged bosons coupled to a Chern-Simons gauge field. Path integral techniques are used to obtain an effective action for the particle density of the system dressed with quantum fluctuations of the CS gauge field. From the action thus obtained we compute the U (1) current of the theory for an arbitrary electromagnetic external field. For the particular case of a homogeneous external magnetic field, we show that the quantization of the transverse conductivity is exact, even in the presence of an arbitrary impurity distribution. The relevance of edge states in this context is analyzed. The propagator of density fluctuations is computed, and an effective action for the matter density in the presence of a vortex excitation is suggested.

Using the noncommuting nature of fermionic fields we obtain a nonperturbative method to calculate the high temperature limit of the grand canonical partition function of interacting fermionic models. This nonperturbative approach is applied to the Hubbard model in d=2(1+1) and we recover the known results in the limit T → ∞.

We found that when the spinless model is off the half-filling regime (µ V ), the Helmholtz free energy (HFE) can be written as two β-expansions: one expansion comes from the half-filling configuration and another one that depends on the parameter x = µ − V . We show numerically that the chemical potential as a function of temperature satisfies a relation similar to the one derived from the particle-hole symmetry of the fermionic spinless model. We extend the β-expansion of the HFE of the one-dimensional fermionic spinless Hubbard model up to order β 8 .