Density of states of the XY model: An energy landscape approach

Cesare Nardini, Rachele Nerattini, Lapo Casetti*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Among the stationary configurations of the Hamiltonian of a classical O(n) lattice spin model, a class can be identified which is in one-to-one correspondence with all the configurations of an Ising model defined on the same lattice and with the same interactions. Starting from this observation it has been recently proposed that the microcanonical density of states of an O(n) model could be written in terms of the density of states of the corresponding Ising model. Later, it has been shown that a relation of this kind holds exactly for two solvable models, the mean-field and the one-dimensional XY model, respectively. We apply the same strategy to derive explicit, albeit approximate, expressions for the density of states of the two-dimensional XY model with nearest-neighbor interactions on a square lattice. The caloric curve and the specific heat as a function of the energy density are calculated and compared against simulation data, yielding a good agreement over the entire energy density range. (C) 2014 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)229-245
Number of pages17
JournalPhysica a-Statistical mechanics and its applications
Publication statusPublished - 15 Feb 2015


  • Lattice spin models
  • Density of states
  • Phase transitions
  • Energy landscapes


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