Progressive quenching - Globally coupled model

TL;DR

This paper investigates a global interaction model where elements are progressively fixed, revealing a martingale property that influences the system's final magnetization distribution, especially near critical points.

Contribution

It introduces a progressive quenching process in a globally coupled Ising model and uncovers its martingale property affecting the system's evolution and final state.

Findings

Final magnetization distribution is non-Gaussian.

System exhibits slow transient scaling.

Martingale property governs the evolution.

Abstract

We study the processes in which fluctuating elements of a system are progressively fixed (quenched) while keeping the interaction with the remaining unfixed elements. If the interaction is global among the Ising spin elements and if the unfixed part is re-equilibrated each time after fixing an element, the evolution of large system is martingale about the equilibrium spin value of the unfixed spins. Due to this property the system starting from the critical point yields the final magnetization whose distribution shows non-Gaussian and slow transient scaling with the system.