Finite range renormalization group to analyze the phase transition caused by long range interactions

2015 Fiscal Year Final Research Report

• Project/Area Number: 25610103
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Kanazawa University
• Principal Investigator: Aoki Ken-Ichi 金沢大学, 数物科学系, 教授 (00150912)
• Co-Investigator(Renkei-kenkyūsha): KOBAYASHI TAMAO 米子高等工業専門学校, 講師 (60506822)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: くりこみ群 / 長距離相互作用 / 機械学習 / 非摂動繰り込み群 / イジング模型 / 相転移 / 自発的対称性の破れ / 制限ボルツマン機械

Outline of Final Research Achievements

One dimensional Ising spin chain with long range interactions is analyzed. In contrast to the nearest neighbor coupling model, the long range model exhibits the spontaneous magnetization with a finite coupling constant.It is also regarded as a simplest model of the quantum dissipation, and the deeper understanding of the dynamics is desired.
We adopt the deep learning method with the restricted Boltzman machine. We set up the unsupervised stochastic learning procedure to make the machine to reproduce the configuration ensembles of the long range Ising model. We calculate the magnetic susceptibility given by the set of configurations generated by the optimized machine and compare the results with the exact evaluation by the block decimation renormalization group, and we got satisfactory equivalence.

Free Research Field

素粒子論