Density of states of continuous and discrete spin models: a case study
arXiv:1110.1276 · doi:10.1088/1742-5468/2012/02/P02007
Abstract
A relation between O(n) lattice spin models and Ising models defined on the same lattice was recently put forward [L. Casetti, C. Nardini, and R. Nerattini, Phys. Rev. Lett. 106, 057208 (2011)]. Such a relation, inspired by an energy landscape analysis, implies that the density of states of an O(n) spin model on a lattice can be effectively approximated, at least close to the phase transition, in terms of the density of states of an Ising model defined on the same lattice and with the same interactions. In the present paper we show that such a relation exactly holds, albeit in a slightly modified form, in the special cases of the mean-field XY model and of the one-dimensional XY model. We also discuss the possible consequences of this result for the general case.
References in corpus (8)
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Phase transitions and configuration space topology
- Finding All the Stationary Points of a Potential Energy Landscape via Numerical Polynomial Homotopy Continuation Method
- Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian
- Phase transitions induced by saddle points of vanishing curvature
- Nonanalyticities of the entropy induced by saddle points of the potential energy landscape
- Kinetic energy and microcanonical nonanalyticities in finite and infinite systems
- On a microcanonical relation between continuous and discrete spin models