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Status: Unchecked ×Keyword: discretization of continuous variables ×Clear all

3 claims from 1 paper

1. Physics and Astronomy › Theoretical and Computational Physics

   Approximating the XY model on a random graph with a q -state clock model

   Lupo and Ricci‐Tersenghi · Physical review. B./Physical review. B · 2017

   The authors show that the q-state clock model approximates the XY model on random graphs with exponentially fast convergence in q, and use this to compute phase diagrams and study replica symmetry breaking.

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   1. Unchecked“It is found that the convergence of physical observables is exponentially fast in the number $q$ of states of the clock model, so allowing a very reliable approximation of the XY model by using a rather small number of states.”
   2. UncheckedIn this study, the exponentially fast convergence of the q-state clock model towards the XY model does not depend on the disorder distribution used.“Furthermore, such an exponential convergence is found to be independent from the disorder distribution used.”
   3. UncheckedIn the XY model on a random graph at zero temperature, replica symmetry breaking occurs for any amount of disorder, however small.“We find that, at zero temperature, spontaneous replica symmetry breaking takes place for any amount of disorder, even an infinitesimal one.”