相关论文: Simple spin models with non-concave entropies
Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and…
For the spherical model with nearest-neighbour interactions, the microcanonical entropy s(e,m) is computed analytically in the thermodynamic limit for all accessible values of the energy e and the magnetization m per spin. The entropy…
We derive the thermodynamic entropy of the mean field $\phi^{6}$ spin model in the framework of the micro-canonical ensemble as a function of the energy and magnetization. Using the theory of large deviations and Rugh's micro-canonical…
It is well-known that the entropy of the microcanonical ensemble cannot be calculated as the Legendre transform of the canonical free energy when the entropy is nonconcave. To circumvent this problem, a generalization of the canonical…
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…
We calculate the thermodynamic entropy of the mean-field $\phi^4$ spin model in the microcanonical ensemble as a function of the energy and magnetization of the model. The entropy and its derivative are obtained from the theory of large…
We study the problem of ensemble equivalence in spin systems with short-range interactions under the existence of a first-order phase transition. The spherical model with nonlinear nearest-neighbour interactions is solved exactly both for…
Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the…
Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: 1)Stirling approximation can be used to evaluate the number of microstates; 2) the surface entropy…
We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics - namely, thermodynamics, equilibrium macrostates, and…
The equivalence of thermodynamic results in the canonical and the microcanonical ensembles has been questioned in some calculations for spin models with long-range interactions. We show that these claims of inequivalence are related to an…
A two-temperature linear spin model is presented that allows an easily understandable introduction to non-equilibrium statistical physics. The model is one that includes the concepts that are typical of more realistic non-equilibrium models…
In this paper, we draw attention to the problem of phase transitions in systems with locally affine microcanonical entropy, in which partial equivalence of (microcanonical and canonical) ensembles is observed. We focus on a very simple spin…
The microcanonical ensemble has long been a starting point for the development of thermodynamics from statistical mechanics. However, this approach presents two problems. First, it predicts that the entropy is only defined on a discrete set…
The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the…
In contrast to the canonical case, microcanonical thermodynamic functions can show nonanalyticities also for finite systems. In this paper we contribute to the understanding of these nonanalyticities by working out the relation between…
Spin models are used in many studies of complex systems---be it condensed matter physics, neural networks, or economics---as they exhibit rich macroscopic behaviour despite their microscopic simplicity. Here we prove that all the physics of…
The microcanonical entropy s(e,m) as a function of the energy e and the magnetization m is computed analytically for the anisotropic quantum Heisenberg model with Curie-Weiss-type interactions. The result shows a number of interesting…
Physical quantities obtained from the microcanonical entropy surfaces of classical spin systems show typical features of phase transitions already in finite systems. It is demonstrated that the singular behaviour of the microcanonically…
We consider here the problem of a "giant spin", with spin quantum number S>>1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic…