Neural Networks for Identifying Phase Transitions

Authors

  • Ana Gabriela da Silva Freitas Universidade do Estado do Rio de Janeiro
  • Kalai Santana Costa Guimarães Universidade do Estado do Rio de Janeiro
  • Zochil Gonzalez Arenas Universidade do Estado do Rio de Janeiro
  • Roberto Santana Grupo de Sistemas Inteligentes ISG, Universidade do País Basco UPV/EHU, Espanha

DOI:

https://doi.org/10.14295/vetor.v35i1.18372

Keywords:

Phase Transitions, Machine Learning, Ising Model

Abstract

In the present work, an introduction was provided to the use of machine learning techniques for identifying the phases of a magnetic system and the transition between these phases. For this, the two-dimensional Ising Model was used, and a single-layer Perceptron network was implemented. The results obtained indicated good accuracy in detecting the phase transition temperature in this model, confirming the feasibility of employing these techniques in the study of phase transitions.

Downloads

References

B. A. Cipra, “An Introduction to the Ising Model,” American Mathematical Monthly, vol. 94, pp. 937–959, 1987. Disponível em: https://doi.org/10.1080/00029890.1987.12000742

Z. G. Arenas, D. G. Barci, e M. V. Moreno, “Path integral approach to nonequilibrium potentials in multiplicative Langevin dynamics,” Europhysics Letters, vol. 113, p. 10009, 2016. Disponível em: https://doi.org/10.1209/0295-5075/113/10009

O. Carrillo, M. Ibañes, J. García-Ojalvo, J. Casademunt, e J. M. Sancho, “Intrinsic noise-induced phase transitions: Beyond the noise interpretation,” Physical Review E, vol. 67, no. 4, p. 046110, 2003. Disponível em: https://doi.org/10.1103/PhysRevE.67.046110

J. Carrasquilla e R. Melko, “Machine learning phases of matter,” Nature Physics, vol. 13, pp. 431–434, 2017. Disponível em: https://doi.org/10.1038/nphys4035

L. Saitta, A. Giordana, e A. Cornuéjols, Phase Transitions in Machine Learning. Cambridge University Press, 2011. Disponível em: https://doi.org/10.1017/CBO9780511975509

K. Shiina, H. Mori, Y. Okabe, e H. K. Lee, “Machine-Learning Studies on Spin Models,” Scientific Reports, vol. 10, p. 2177, 2020. Disponível em: https://doi.org/10.1038/s41598-020-58263-5

D. A. Stariolo e S. A. Cannas, Mecânica Estatística e Fenômenos Críticos: uma introdução. Editora Livraria da Física, 2023.

L. Onsager, “Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition,” Physical Review, vol. 65, pp. 117–149, Feb 1944. Disponível em: https://doi.org/10.1103/PhysRev.65.117

Published

2025-04-01

How to Cite

Freitas, A. G. da S., Guimarães, K. S. C., Arenas, Z. G., & Santana, R. (2025). Neural Networks for Identifying Phase Transitions. VETOR - Journal of Exact Sciences and Engineering, 35(1), e18372. https://doi.org/10.14295/vetor.v35i1.18372

Issue

Section

Special Section XXVII ENMC/XV ECTM
Crossref
0
Scopus
0