This section is prepared for the pedagogical exploration of magnetic models within statistical mechanics. Rather than generating novel scientific data, these applications aim to allow students and researchers to interactively explore the behaviour of spin systems under temperature, external magnetic fields and various interactions.
All simulations are designed entirely client-side to avoid server load and run natively in your browser using JavaScript. Each simulation opens in a new tab.
Comprehensive labs that work step by step through fundamental topics of statistical physics and magnetism, with detailed explanations, suggested experiments and comparisons with exact results. Each lab describes its own scope and limitations on its page.
The same model is solved with the Metropolis, heat-bath, Wolff and Swendsen–Wang algorithms, and the correlation between samples and the error bars are measured. Phase transitions are located with the Binder cumulant crossing and finite-size scaling; the Mermin–Wagner theorem, the BKT transition and first-order transitions are explored.
Open LabThrough the imaginary-time path integral, a d-dimensional quantum system becomes a (d+1)-dimensional classical one whose world lines are sampled. Quantum phase transitions are located with continuous-time and SSE/directed-loop methods and compared with exact solutions; the sign problem is shown on a frustrated lattice.
Open LabThe static structure factor of a magnetic configuration is the set of weights of the plane waves that make it up. Bragg peaks are split into longitudinal and transverse components, and the configuration is rebuilt by picking the peaks one by one and superposing the waves. Modulation, harmonics and the effect of disorder on the peak shape are explored.
Open LabHow a small deviation propagates through a ferromagnet or an antiferromagnet as a wave. The full (nonlinear) Landau–Lifshitz equation is solved and compared with linear spin-wave theory; the effects of anisotropy, DMI and thermal magnons are explored.
Open LabThe quantum counterpart of the classical spin wave: a single magnon, the interaction and bound states of two magnons, and the Néel state melting under quantum fluctuations into spinons. Exact numerical results are shown side by side with approximate theories such as Holstein–Primakoff/Bogoliubov. Best used together with the Spin Wave Laboratory.
Open LabShorter, focused simulations related to the research topics of our group (magnetic skyrmions and topological spin textures).
Visualization of skyrmions, antiskyrmions, skyrmioniums, merons and bimerons in terms of polarity, vorticity and helicity, and of their wrapping of the unit sphere.
Launch SimulationMonte Carlo nucleation of spin cycloids, helices, and magnetic skyrmions with quantized topological charges under Néel and Bloch type chiral interactions.
Launch SimulationConcurrent spin evolution on a triangular lattice with thermal Langevin noise and DMI, solved via the Heun integrator.
Launch SimulationExcitation of the CCW, breathing and CW spin-wave modes of a skyrmion lattice by a sinusoidal magnetic field; resonance, rotation-selective excitation and spectrum measurement.
Launch SimulationDrift of a skyrmion in a spatially varying magnetic field, the skyrmion Hall effect and comparison with the Thiele equation; interaction between skyrmions.
Launch SimulationShort, single-screen demonstrations of basic models. For a detailed treatment of these models and more, see the Classical Monte Carlo Lab.
Investigation of thermal evolution, phase transitions, magnetic susceptibility, and specific heat fluctuations of discrete (±1) spins on a square lattice.
Launch SimulationObservation of the dynamics of continuous (3D vector) spin systems under external fields and the Mermin-Wagner theorem via finite-size effects.
Launch Simulation