Progressive quenching - Globally coupled model

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 Ising spin elements and if the unfixed part is re-equilibrated each time after fixing an element, the evolution of a 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 behavior with the system size.

Progressive Quenching --- Ising Chain Models

“…The evident source of the equilibrium ensemble is that, in our protocol, the unquenched part of the system is equilibrated before the quenching of spin or spins and, moreover, the spatial Markovian nature of the equilibrium fluctuations should be essential. In the case of globally coupled Ising model [3], the ensemble generated by the Pq is qualitatively different from the equilibrium one. In the latter case, however, there emerged a quasi-martingale property in the unquenched equilibrium spin, m T in their notation, which reflect the fact that the quenching is done as a snapshot of the equilibrium state.…”

“…What is in common between the present progressive quenching (Pq) and the study in [3] is the way we fixed the spins: We did it as a snapshot of the equilibrium state. For the Ising chains with the interaction with the nearest neighbor or up to the second nearest neighbor spins, we found that Pq of a single spin or a pair of neighboring spins generates the ensemble of spin configurations which is identical to the equilibrium ensemble of the given system.…”

“…Very recently, one of the authors studied the Pq of the globally coupled spin model [3]. They observed the emergence of a martingale property.…”