Oscillating hysteresis in the q-neighbor Ising model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Complex Systems

Background:

• The kinetic Ising model is a fundamental tool for studying magnetism and phase transitions.
• Understanding how interaction topology affects phase transitions is crucial in statistical physics.

Purpose of the Study:

• To investigate the impact of random q-spin interactions on the kinetic Ising model.
• To analyze the nature of phase transitions and hysteresis in this modified model.
• To explore potential evidence for mixed-order phase transitions.

Main Methods:

• Modification of the kinetic Ising model with Metropolis dynamics.
• Introduction of random q-spin interactions, simulating a complete graph topology.
• Analytical derivation of transition probabilities due to the mean-field-like nature.
• Calculation of order parameter probability density functions and effective potentials.

Main Results:

• A phase transition occurs for q≥3, with critical temperature T* increasing linearly with q.
• The transition is continuous for q=3 and discontinuous for q>3.
• Hysteresis exhibits oscillatory behavior for q>3 (expanding for even q, shrinking for odd q).
• The model allows for precise determination of hysteresis and effective potentials with distinct steady states.

Conclusions:

• A minor alteration to the kinetic Ising model significantly changes phase transition dynamics.
• The study reveals a switch from continuous to discontinuous transitions and introduces oscillating hysteresis.
• Observed phenomena for q=5 may indicate a mixed-order phase transition, warranting further investigation.