Virtual walks in the Ising model: finite time scaling

TL;DR

This paper investigates the non-equilibrium dynamics of the Ising model using a novel virtual walk approach, revealing critical behavior and finite time scaling consistent with known critical exponents.

Contribution

It introduces a virtual walk framework based on spin states and local energy, providing new insights into non-equilibrium dynamics and critical scaling in the Ising model.

Findings

Displacement distribution changes with temperature

Detection of a time-dependent critical point

Finite time scaling aligns with known critical exponents

Abstract

The dynamics of the spins in the Ising model are analyzed using a virtual walk scenario. The system is quenched from a very high temperature to a lower one using the Glauber scheme in one and two dimensions. A walk is associated with each spin which evolves according to the current state of the spin. The probability distribution of the displacement is calculated that shows a distinct change as the temperature is increased. The average displacement as a function of time shows a non-equilibrium region stretched over a much longer time interval compared to the bulk magnetization. Nevertheless, one can still detect a time dependent critical point determined by two different methods. In addition, we introduce a virtual walk constructed from the local energy of individual spins. Finite time scaling of the different quantities estimated in two dimensions show excellent consistency with the values of the known critical exponents.