npsm 새물리 New Physics : Sae Mulli

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Research Paper

New Phys.: Sae Mulli 2019; 69: 655-659

Published online June 28, 2019 https://doi.org/10.3938/NPSM.69.655

Copyright © New Physics: Sae Mulli.

Critical Point Estimation of the Two-dimensional Ising Model Using the Multi-Perceptron

다중퍼셉트론을 이용한 이차원 이징 모형의 임계점 계산

Seung-Yeon KIM1, Jaehyung LIM2, Wooseop KWAK3*

1School of Liberal Arts and Sciences, Korea National University of Transportation, Chungju 27469, Korea

2Department of Physics, Chosun University, Gwangju 61452, Korea
3Department of Physics, Chosun University, Gwangju 61452, Korea

Correspondence to:wkwak@chosun.ac.kr

Received: April 15, 2019; Revised: May 2, 2019; Accepted: May 3, 2019

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The ordered states and the disordered states of the two-dimensional Ising model are studied by using the gradient descent method, which minimizes the error function in the multi-perceptron. The data obtained from simulations using the well-learned multi-perceptron and those obtained from simulations using the Wang-landau sampling method are compared with data obtained using the finite size scaling method. The critical temperatures, ${T_\text{c}}_\text{MP}(\infty)=2.26357 \pm 0.005024$ and ${T_\text{c}}_\text{WL}(\infty)=2.26224 \pm 0.00222144$, are obtained from multi-perceptron and from the Wang-Landau sampling method, respectively. These results show that the well-learned multi-perceptron can properly estimate the critical temperature of the Ising model.

Keywords: Critical point, Ising model, Multi-perceptron, Magnetic susceptibility

이차원 사각격자에서의 이징모형 (Ising model)의 질서적인상태와 무질서적인상태를 길이차원 $L= 4, 6, 8, 10, 12$ 에서 다층 퍼셉트론에 오차함수를 최소화 하는 경사 하강법 방법으로 학습시켰다. 잘 학습된 다층 퍼셉트론(Multi-Perceptron)에 몬테칼로 전산시늉을 이용하여 만든 이징모형 (Ising model) 데이터를 입력하였을 때 나오는 시그모이드 함수 결과 값과 왕-란다우 표본잡기(Wang-Landau Sampling)를 사용한 몬테칼로 전산시늉 데이터를 이용하여 만든 이징모델 데이터의 자화율의 임계온도를 유한크기 눈금잡기 방법을 이용해 비교해 보았을 때 각각 계산된 자화율의 임계온도는 ${T_\text{c}}_\text{MP}(\infty)=2.26357 \pm 0.005024$ 과 ${T_\text{c}}_\text{WL}(\infty)=2.26224 \pm 0.00222144$ 로 나타났다. 이에 우리는 잘 학습된 다층 퍼셉트론이 만들어낸 자화율에 대한 결과 값을 가지고 이를 이용한 유한크기 눈금잡기 방법을 통하여 임계온도를 적절히 유추 할 수 있음을 알게 되었다.

Keywords: 임계점, 이징모형, 다층 퍼셉트론, 자기감수율

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