Window measurements of simulations in random systems

TL;DR

This paper introduces a window-measurement method to mitigate finite-size and boundary effects in numerical studies of random systems, enabling more accurate scaling analysis.

Contribution

The paper presents a practical window-measurement technique that reduces correction-to-scaling effects, validated on a 3D Heisenberg spin glass model.

Findings

Data collapse onto a single scaling function across system sizes.

Transition temperatures for spin-glass and chiral-glass are very close.

Correction-to-scaling terms are significantly minimized.

Abstract

Numerical studies in random systems are plagued with strong finite-size effects and boundary effects. We introduce a window-measurement method as a practical solution to these difficulties. We observe physical quantities only within a subsystem located in the midst of a whole system and scale them with the correlation length estimated in the subsystem. Both equilibrium data and nonequilibrium data with different system sizes and different window sizes fall onto a single scaling function. It suggests that the correction-to-scaling terms become very small. We confirm the validity in the $\pm J$ Heisenberg spin glass model in three dimensions. The spin-glass and chiral-glass transition temperatures are estimated to be very close to each other.