Virtual walks in the Ising model: Finite-time scaling

Area of Science:

• Statistical Mechanics
• Computational Physics
• Condensed Matter Physics

Background:

• The Ising model is a fundamental model in statistical mechanics for studying magnetism and phase transitions.
• Understanding spin dynamics under non-equilibrium conditions is crucial for various physical phenomena.

Purpose of the Study:

• To analyze the dynamics of spins in the Ising model using a novel virtual walk scenario.
• To investigate the system's behavior when quenched from high to low temperatures.
• To explore non-equilibrium phenomena and estimate critical points.

Main Methods:

• A virtual walk scenario is employed, where each spin's evolution is tied to its current state.
• The Glauber scheme is used for quenching the system in one and two dimensions.
• Probability distributions of walker displacement and average displacement over time are calculated.
• Finite-time scaling analysis is applied to quantities in two dimensions.

Main Results:

• A distinct change in the probability distribution of walker displacement is observed with increasing temperature.
• A non-equilibrium region in average displacement persists longer than bulk magnetization.
• A time-dependent critical point can be estimated using two distinct methods.
• Virtual walks generated from local spin energy are introduced.
• Finite-time scaling in 2D shows consistency with known critical exponents.

Conclusions:

• The virtual walk method provides a valuable tool for studying non-equilibrium dynamics in the Ising model.
• The approach allows for the detection and estimation of critical phenomena even in finite time.
• Results validate the consistency of the virtual walk method with established critical exponent values.