Fluctuation-dominated phase ordering at a mixed order transition

Abstract

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.

References in corpus (21)

• Theory of Phase Ordering Kinetics
• Nontrivial Exponent for Simple Diffusion
• The Nature of the Condensate in Mass Transport Models
• Jamming Percolation and Glass Transitions in Lattice Models
• Canonical Analysis of Condensation in Factorised Steady State
• Core percolation on complex networks
• Discontinuous Percolation Transitions in Epidemic Processes, Surface Depinning in Random Media and Hamiltonian Random Graphs
• Active nematics are intrinsically phase-separated
• Spatial Structures and Giant Number Fluctuations in Models of Active Matter
• Particles Sliding on a Fluctuating Surface: Phase Separation and Power Laws
• Strong Phase Separation in a Model of Sedimenting Lattices
• Anomalous discontinuity at the percolation critical point of active gels
• Phase segregation of passive advective particles in an active medium
• Exact extreme value statistics at mixed order transitions
• Violation of Porod law in a freely cooling granular gas in one dimension
• Extraordinary variability and sharp transitions in a maximally frustrated dynamic network
• Large compact clusters and fast dynamics in coupled nonequilibrium systems
• Dynamics of Fluctuation Dominated Phase Ordering: Hard-core Passive Sliders on a Fluctuating Surface
• Ordered phases in coupled nonequilibrium systems: static properties
• Longest interval between zeros of the tied-down random walk, the Brownian bridge and related renewal processes
• Order parameter scaling in fluctuation dominated phase ordering

Cited by in corpus (10)

• Extreme value statistics of correlated random variables: a pedagogical review
• $BKT$ transitions in classical and quantum long-range systems
• Condensation and extremes for a fluctuating number of independent random variables
• Light and heavy particles on a fluctuating surface: Bunchwise balance, irreducible sequences and local density-height correlations
• Size-Stretched Exponential Relaxation in a Model with Arrested States
• Comment on `Fluctuation-dominated phase ordering at a mixed order transition'
• Thermodynamic phases in first detected return times of quantum many-body systems
• Fluctuation dominated phase ordering in coarse-grained depth models: Domain wall structures, extreme values and coarsening
• Critical dynamics of long range models on Dynamical Lévy Lattices
• Preface: Long-range Interactions and Synchronization