Zero Temperature Dynamics of 2D and 3D Ising Ferromagnets

TL;DR

This paper investigates the zero-temperature dynamics of 2D and 3D Ising ferromagnets, analyzing how initial configurations influence the system's convergence to frozen states and exploring complex phenomena like striped and blinker states.

Contribution

It provides new insights into the convergence behavior of 2D and 3D Ising models at zero temperature, including relations between initial conditions and final states, and characterizes complex metastable configurations.

Findings

System converges to frozen states when initial spin bias p ≠ 1/2.

For p=1/2 in 3D, the system likely does not reach a fully frozen state.

Identified and analyzed properties of striped and blinker states.

Abstract

We consider zero-temperature, stochastic Ising models with nearest-neighbor interactions in two and three dimensions. Using both symmetric and asymmetric initial configurations, we study the evolution of the system with time. We examine the issue of convergence of the dynamics and discuss the nature of the final state of the system. By determining a relation between the median number of spin flips per site, the probability p that a spin in the initial spin configuration takes the value +1, and lattice size, we conclude that in two and three dimensions, the system converges to a frozen (but not necessarily uniform) state when p is not equal to 1/2. Results for p=1/2 in three dimensions are consistent with the conjecture that the system does not evolve towards a fully frozen limiting state. Our simulations also uncover `striped' and `blinker' states first discussed by Spirin et al., and their statistical properties are investigated.