Rigorous Calculation of the Partition Function for the Finite Number of Ising Spins

TL;DR

This paper presents a scalable parallel algorithm in C++ for rigorously calculating the partition function of finite Ising spin systems in 2D and 3D, enabling precise analysis of interacting spin models.

Contribution

The authors developed a high-performance parallel algorithm using MPI for exact partition function calculations in finite Ising models, with demonstrated scalability and super-linear speedup.

Findings

Algorithm achieves super-linear speedup for small process counts.

Scalability analyzed on various parallel and distributed systems.

Applicable to research of complex Ising spin systems with interactions.

Abstract

The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing Interface and massive parallel instructions. The algorithm can be used for the research of the interacting spin systems in the Ising models of 2D and 3D. The processing power and scalability is analyzed for different parallel and distributed systems. Different methods of the speed up measuring allow obtain the super-linear speeding up for the small number of processes. Program code could be useful also for research by exact method of different Ising spin systems, e.g. system with competition interactions.