A study on Arctic sea ice dynamics using the continuous spin Ising model

Abstract

The Ising model, initially proposed about 100 years ago to explain ferromagnetism and phase transitions, has become a central pillar of statistical physics and a powerful tool for diverse applications in other fields including environmental studies. In this paper, we introduce continuous spin values between −1 and +1 to a two-dimensional Ising model and utilize the generalized Ising lattice to simulate the dynamics of sea ice/water transition for a large area of 1500 km by 1500 km in the Arctic region. The simulation process follows the Metropolis-Hastings algorithm and incorporates an innovative factor to account for the inertia of spin value changes. Using the sea ice concentration data collected by the National Snow and Ice Data Center, our results exhibit striking similarity between the simulated and the observed ice melting and freezing dynamics, and two numerical measures from the simulation—the ice coverage percentage and the ice extent—match closely with the data statistics. Moreover, the model's best-fit parameters demonstrate the substantial impact of the external forces, which can be further enriched and linked to the environmental factors in other climate change research.