Back to overview

Monte Carlo simulation of the transverse-field Ising model

A worldline view of the one-dimensional quantum Ising chain, with temperature and transverse field exposed through the same control language used across the demo set.

Actions

Controls

Temperature: T / J = 0.10 Transverse field: Gamma / J = 1.00

Explanation

This page visualizes the one-dimensional transverse-field Ising model, \[ H = -J \sum_{i=1}^{N} \sigma_i^z \sigma_{i+1}^z - \Gamma \sum_{i=1}^{N} \sigma_i^x \] using a continuous-imaginary-time Monte Carlo representation.

Each vertical strip corresponds to one spin in real space, while the vertical direction represents imaginary time. Purple and white segments indicate opposite \(\sigma^z\) orientations.

Adjust the temperature and transverse field to see how kink density and temporal ordering change. The system uses periodic boundary conditions with \(L = 100\).