Thinning algorithms for the Monte Carlo simulation of kinetic Ising models

Area of Science:

• Computational Physics
• Statistical Mechanics
• Materials Science

Background:

• Kinetic Ising models (KIMs) are crucial for understanding phase transitions and metastability.
• Simulating long-timescale dynamics in KIMs, especially with Glauber spin-flip dynamics, presents significant computational challenges.
• Nonhomogeneous Poisson processes (NHPPs) are often used to model event occurrences in time-dependent systems.

Purpose of the Study:

• To adapt the thinning method for numerically generating NHPP arrival times.
• To accelerate Monte Carlo simulations of KIMs, particularly for metastable state decay and hysteresis.
• To enable simulations of phenomena at previously inaccessible timescales and frequencies.

Main Methods:

• Adaptation of the thinning method for NHPPs to accelerate KIM simulations.
• Implementation of thinning using piecewise-constant majorizing functions.
• Simulation of metastable state decay in stationary KIMs.
• Simulation of KIM hysteresis in a periodic external field.

Main Results:

• The adapted thinning method significantly accelerates Monte Carlo simulations of KIMs.
• Simulations achieved unprecedented timescales for metastable state decay (lifetimes many orders of magnitude longer).
• Hysteresis was simulated at frequencies in the tens of nanohertz, extending to practical low temperatures.

Conclusions:

• The developed algorithms provide a powerful tool for simulating complex dynamics in KIMs.
• This acceleration opens new avenues for studying metastability and hysteresis in materials science.
• The method's applicability at practical temperatures makes it relevant for various applications, including hyperthermia research.