Year: 2020
Type: article
Abstract: We present a Markov chain Monte-Carlo (MCMC) method to make a geometric graph which satisfies the following two conditions: (i) The degree of each vertex is fixed to a positive integer $k$. (ii) The probability that two vertices located on a $d$-dimensional hypercubic lattice are connected by an edge is proportional to $d_{ij}^{-α}$, where $d_{ij}$ is the distance between the two vertices and $α$ is a positive exponent. We introduce a reverse update method and a list-based update method for the MCMC method. The graph is updated efficiently by the MCMC method since the two update methods work complementarily. We also investigate a ferromagnetic Ising model defined on the geometric graph as a test case. As a result, we have confirmed that the nature of ferromagnetic transition significantly depends on the exponent $α$.
Author: Munetaka Sasaki
Institution: Kanagawa University
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3014339135