Interactive Plotly visualizations

Every other visualizer in physicskit.statphys is Matplotlib-based: static, ideal for publication figures and this documentation’s gallery. physicskit.statphys.visualizers.interactive renders the same information as pan/zoom/hover-enabled Plotly figures instead, convenient for interactively exploring a parameter sweep or a dense vector field in a Jupyter notebook. This example builds one such figure for each of three lattice/particle models used throughout this gallery – the 2D Ising ferromagnet, the 2D XY model, and a Lennard-Jones gas – and saves each as a standalone HTML file.

import numpy as np

from physicskit.statphys.chapters.ising_lattice import Ising2D, XYModel2D
from physicskit.statphys.chapters.molecular_dynamics import LennardJonesGas
from physicskit.statphys.visualizers.interactive import (
    interactive_particle_snapshot,
    interactive_temperature_sweep,
    interactive_vortex_field,
)

An interactive temperature sweep

The 2D Ising ferromagnet, \(H = -J \sum_{\langle i,j \rangle} s_i s_j\) with \(s_i = \pm 1\) on a periodic \(L \times L\) lattice, is swept in temperature across its critical point \(T_C\) with the Wolff cluster algorithm; the resulting figure lets you hover over the energy, order parameter, specific heat, and susceptibility curves.

model = Ising2D(L=20, seed=0)
temperatures = np.linspace(model.T_C - 1.0, model.T_C + 1.0, 10)
result = model.run_temperature_sweep(temperatures, n_equil=100, n_measure=150, algorithm="wolff")
fig = interactive_temperature_sweep(result, T_c=model.T_C)
fig.write_html("ising_sweep_interactive.html")

An interactive vortex field

The 2D XY model, \(H = -J \sum_{\langle i,j \rangle} \cos(\theta_i - \theta_j)\) with continuous planar spin angles \(\theta_i\), is equilibrated exactly at its Kosterlitz-Thouless transition temperature \(T_{\text{KT}}\), where bound vortex-antivortex pairs are just beginning to unbind; the interactive field lets you pan and zoom into individual vortex cores.

xy_model = XYModel2D(L=20, seed=1)
xy_model.sweep(beta=1.0 / xy_model.T_KT, n_sweeps=300)
fig = interactive_vortex_field(xy_model.theta)
fig.write_html("xy_vortices_interactive.html")

An interactive particle snapshot

A 2D gas of \(N=100\) particles interacting through the Lennard-Jones potential \(V(r) = 4\epsilon[(\sigma/r)^{12} - (\sigma/r)^{6}]\) is integrated forward in a periodic box; the interactive scatter plot colors each particle by its instantaneous speed, hoverable per-particle.

gas = LennardJonesGas(n_particles=100, box_size=15.0, seed=2)
gas.step(n_steps=500)
fig = interactive_particle_snapshot(gas)
fig.write_html("lj_gas_interactive.html")

print("Wrote 3 standalone interactive HTML files.")

Wrote 3 standalone interactive HTML files.