pISSN 0374-4914 eISSN 2289-0041

Research Paper

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

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

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

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