2011/10/31 by Cesare Nardini, Rachele Nerattini, Lapo Casetti · 6 citations
Mathematics · Physics and Astronomy · #Classical XY model #Condensed matter physics #Ising model #Lattice (music) #Mathematical physics #Mathematics #Mean field theory #Opinion Dynamics and Social Influence #Phase transition #Physics #Quantum many-body systems #Quantum mechanics #Statistical physics #Theoretical and Computational Physics #Theoretical physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2012/02/p02007
published in Journal of Statistical Mechanics Theory and Experiment 2012(02), P02007 (Institute of Physics)
openalex publication_date 2012/02/09 · arxiv created 2012/02/13 · arxiv updated 2012/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A relation between O ( n ) lattice spin models and Ising models defined on the same lattice was recently put forward (Casetti et al 2011 Phys. Rev. Lett. 106 057208). 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 this 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 the one-dimensional XY model. We also discuss the possible consequences of this result for the general case.