Abstract
A generalization of the original Gibbs phase rule is proposed in order to study the presence of single phases, multiphase coexistence, and multicritical phenomena in lattice spin magnetic models. The rule is based on counting the thermodynamic number of degrees of freedom, which strongly depends on the external fields needed to break the ground state degeneracy of the model. The phase diagrams of some spin Hamiltonians are analyzed according to this general phase rule, including general spin Ising and Blume–Capel models, as well as q-state Potts models. It is shown that by properly taking into account the intensive fields of the model in study, the generalized Gibbs phase rule furnishes a good description of the possible topology of the corresponding phase diagram. Although this scheme is unfortunately not able to locate the phase boundaries, it is quite useful to at least provide a good description regarding the possible presence of critical and multicritical surfaces, as well as isolated multicritical points.
Highlights
Just a few years after Andrews’ experimental discovery of the critical opalescence in carbon dioxide [1], Gibbs introduced the phase rule [2,3]
The so-called Gibbs phase rule (GPR) is solely based on general thermodynamics arguments and can give a remarkable account of the possible number of phases that can coexist for a given system, as well as how many of them can become equal at certain conditions
In the temperature–pressure plane, a pure substance can present a line of two coexisting phases, points where three phases coexist, and points where two phases can become equal. This is in remarkable agreement with the experimental phase diagram of single compounds, where one has lines of gas-liquid, gas-solid, and liquid-solid coexisting phases, only one triple point, and one critical point
Summary
Just a few years after Andrews’ experimental discovery of the critical opalescence in carbon dioxide (which Andrews himself coined as the critical point) [1], Gibbs introduced the phase rule [2,3]. GPR is violated and apply it to some known spin Hamiltonian models showing that the corresponding phase diagrams are in agreement with this more fundamental thermodynamic behavior. This is achieved by properly taking into account the external fields needed to break the degeneracy of the ground states of the system in order to compute the desired thermodynamic number of degrees of freedom. It turns out that such a phase rule could be quite useful in the study of more complex models It will allow the proper description of the phases, the phase coexistence, and the corresponding critical and multicritical behavior present in these systems (which, as we will see below, are sometimes still misnamed and not suitably characterized in the literature).
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