  There are problems with defining the thermodynamic limit of systems with
long-range interactions; as a result, the thermodynamic behavior of these types
of systems is anomalous. In the present work, we review some concepts from both
extensive and nonextensive thermodynamic perspectives. We use a model, whose
Hamiltonian takes into account spins ferromagnetically coupled in a chain via a
power law that decays at large interparticle distance $r$ as $1/r^{\alpha}$ for
$\alpha\geq0$. Here, we review old nonextensive scaling. In addition, we
propose a new Hamiltonian scaled by $2\frac{(N/2)^{1-\alpha}-1}{1-\alpha}$ that
explicitly includes symmetry of the lattice and dependence on the size, $N$, of
the system. The new approach enabled us to improve upon previous results. A
numerical test is conducted through Monte Carlo simulations. In the model,
periodic boundary conditions are adopted to eliminate surface effects.
