Oscillating hysteresis in the q-neighbor Ising model

Abstract

We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with $q$ spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with $q\ge 3$ exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature $T^{\ast }$, which linearly increases with $q$. Moreover, we show that for $q=3$ the phase transition is continuous and discontinuous for larger values of $q$. For $q>3$ the hysteresis exhibits oscillatory behavior -- expanding for even values of $q$ and shrinking for odd values of $q$. If only simulation results were taken into account, this phenomenon could be mistakenly interpreted as switching from discontinuous to continuous phase transitions or even as evidence of the so-called mixed phase transitions. Due to the mean-field like nature of the model we are able to calculate analytically not only the stationary value of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable and metastable steady states. The main message is that in case of non-equilibrium systems the hysteresis can behave in an odd way and computer simulations alone may mistakenly lead to incorrect conclusions.

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• Characterization of the Nonequilibrium Steady State of a Heterogeneous Nonlinear $q$-Voter Model with Zealotry
• A Heterogeneous Out-of-Equilibrium Nonlinear $q$-Voter Model with Zealotry
• Pair approximation for the $q$-voter model with independence on multiplex networks
• A veritable zoology of successive phase transitions in the asymmetric $q$-voter model on multiplex networks
• Tricriticality in the $q$-neighbor Ising model on a partially duplex clique
• No-enclave percolation corresponds to holes in the cluster backbone
• Kinetic Ising models with various single-spin flip dynamics on quenched and annealed random regular graphs
• Tricritical behavior of nonequilibrium Ising spins in fluctuating environments
• Ferromagnetic and spin-glass like transition in the $q$-neighbor Ising model on random graphs
• Ordering kinetics with long-range interactions: interpolating between voter and Ising models
• $Q$-voter model with independence on signed random graphs: homogeneous approximations
• Mixed-order phase transition in a minimal, diffusion based spin model
• Critical dynamics of long range models on Dynamical Lévy Lattices
• The $q$-neighbor Ising model on multiplex networks with partial overlap of nodes
• q-neighbor Ising model on a polarized network
• Temperature-Noise Interplay in a Coupled Model of Opinion Dynamics
• Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs
• Suppression of discontinuous phase transitions by particle diffusion
• Anomalous finite-size scaling in higher-order processes with absorbing states