Archive ouverte HAL – Fluctuation-dominated phase ordering at a mixed order transition

Mustansir Barma 1 Satya N. Majumdar 2 David Mukamel 3 Satya Majumdar 2

Mustansir Barma, Satya N. Majumdar, David Mukamel, Satya Majumdar. Fluctuation-dominated phase ordering at a mixed order transition. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2019, 52 (25), pp.254001. ⟨10.1088/1751-8121/ab2064⟩. ⟨hal-02291900⟩

Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length. We show that the behaviour of the order parameter correlation function along the transition line of mixed order transitions can change from normal critical behaviour with power law decay, to fluctuation-dominated phase ordering as a parameter is varied. The defining features of fluctuation-dominated order are anomalous fluctuations which remain large in the thermodynamic limit, and correlation functions which approach a finite value through a cusp singularity as the separation scaled by the system size approaches zero. We demonstrate that fluctuation-dominated order sets in along a portion of the transition line of an Ising model with truncated long-range interactions which was earlier shown to exhibit mixed order transitions, and also argue that this connection should hold more generally.

  • 1. Department of Theoretical Physics
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 3. Weizmann Institute