Thermodynamics from a scaling Hamiltonian

[摘要] 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 >= 0. Here, we review old nonextensive scaling. In addition, we propose a Hamiltonian scaled by 2(N/2)(1-alpha)-1/1-alpha that explicitly includes symmetry of the lattice and dependence on the size N of the system. The 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.

[发布日期] 2007-11-01

[关键词] LONG-RANGE INTERACTIONS;NONEXTENSIVE THERMOSTATISTICS;CRITICAL-BEHAVIOR;FERROMAGNETISM;EQUILIBRIUM;MODELS