Macros and Multiscale Dynamics in Spin Glasses

TL;DR

This paper investigates the multiscale dynamics of spin glasses, introduces accelerated algorithms for dilute cases, and discusses challenges in applying multiscale-cluster algorithms to frustrated systems, highlighting fundamental limitations.

Contribution

It presents new accelerated algorithms for dilute spin glasses and analyzes the limitations of multiscale-cluster algorithms in frustrated systems with ultrametric ground states.

Findings

Accelerated algorithms effectively model dilute spin glass dynamics.

Multiscale-cluster algorithms face fundamental limitations in frustrated systems.

Tunneling between vacua cannot be captured by macros-based algorithms in ultrametric spaces.

Abstract

We study the spacial and temporal multiscale properties of complex systems. We present accelerated algorithms for dilute spin glasses and display explicitly their relation to the effective dynamics of specific collective degrees of freedom (macros). We discuss the difficulties in applying multiscale-cluster algorithms(MCA) to general frustrated systems: MCA does not succeed to break the system into clusters. We relate these difficulties to rigorous negative results in systems with an ultrametric space of ground states: the tunneling between vacua cannot be expressed into an algorithm acting upon independent macros.