Simulating thermal boundary conditions of spin-lattice models with weighted averages

TL;DR

This paper introduces a weighted average method for simulating thermal boundary conditions in spin-lattice models, improving efficiency and accuracy over traditional population annealing methods affected by temperature chaos.

Contribution

The paper proposes a novel weighted average approach for thermal boundary conditions, enhancing simulation efficiency and accuracy in disordered spin systems.

Findings

Weighted average method outperforms population annealing in efficiency.

The new method reduces the impact of temperature chaos.

Improved accuracy in simulating boundary conditions.

Abstract

Thermal boundary conditions has played an increasingly important role in revealing the nature of short-range spin glasses and is likely to be relevant also for other disordered systems. Diffusion method initializing each replica with a random boundary condition at the infinite temperature using population annealing has been used in recent large-scale simulations. However, the efficiency of this method can be greatly suppressed because of temperature chaos. For example, most samples have some boundary conditions that are completely eliminated from the population in the process of annealing at low temperatures. In this work, I study a weighted average method to solve this problem by simulating each boundary conditions separately and collect data using weighted averages. The efficiency of the two methods are studied using both population annealing and parallel tempering, showing that the weighted average method is more efficient and accurate.