Hard-Disk Monte Carlo

Background Theory

\begin{equation} \langle X\rangle = \dfrac{\int\text{d}q^{N}\exp\big[-\beta\mathcal{V}(q^{N})\big]X(q^{N})}{\int\text{d}q^{N}~\exp\big[-\beta\mathcal{V}(q^{N})\big]} \end{equation}

Metropolis Criterion

This can be alternatively written down as: \begin{equation} \text{acc}(o\rightarrow n)=\min\bigg(1,\exp\bigg[-\beta\big(\mathcal{V}(n)-\mathcal{V}(o)\big)\bigg]\bigg) \end{equation}

The Code

We want to build a Monte Carlo package in javascript using object-oriented programming

Setting up the System

class System {
  // set initial system parameters
  constructor(){
    this.npart     = 100; // number of particles in the system
    this.density   = 0.4; // density of the system
    this.area      = (this.npart*20**2)/this.density; // area of the simulation box
    this.box_x     = Math.sqrt(this.area); // length of the box along the x-axis
    this.box_y     = this.box_x; // length of the box along the y-axis
    this.particles = []; // list of particles in the system
  }
}

Final Result