Scaling and Universality at Noise-Affected Non-Equilibrium Spin Correlation Functions

TL;DR

This paper explores how uncorrelated noise affects the scaling and universality of non-equilibrium spin correlation functions, revealing noise-induced phenomena and a universal scaling behavior in dynamical phase transitions.

Contribution

It demonstrates the impact of noise on critical sweep velocities, excitation probabilities, and introduces a universal scaling function for spin correlation dynamics.

Findings

Noise decreases the critical sweep velocity linearly with noise strength.

Noise induces a maximally mixed mode with excitation probability 1/2.

A universal scaling function collapses boundary sweep-velocity curves.

Abstract

We investigate scaling and universality in nonequilibrium spin correlation functions in the presence of uncorrelated noise. In the absence of noise, spin correlation functions exhibit a crossover from monotonic decay at fast sweep velocities to oscillatory behavior at slow sweeps. We show that, under a stochastically driven field, the critical sweep velocity at which the spin correlation functions undergo an abrupt change decreases with increasing noise strength and scales linearly with the square of the noise intensity. Remarkably, when the noise intensity and sweep velocity are comparable, the excitation probability becomes locked to pk = 1/2 over a finite momentum window, signaling the emergence of noise-induced maximally mixed modes. This gives rise to a highly oscillatory region in the dynamical phase diagram, whose threshold sweep velocity increases with noise and likewise exhibits quadratic scaling with the noise strength. Finally, we identify a universal scaling function under which all boundary sweep-velocity curves collapse onto a single universal curve.