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Simulate fluctuations and critical fields
Build and assess stochastic simulations of statistical field models through sampling diagnostics, renormalization-sensitive observables, and finite-size extrapolation.
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Module 01 research
Simulate fluctuations and critical fields
Build and assess stochastic simulations of statistical field models through sampling diagnostics, renormalization-sensitive observables, and finite-size extrapolation.
- 01
Metropolis sampling of Ising configurations
Construct a balanced local spin update from an explicitly counted lattice measure and distinguish equilibrium correctness from a finite run.
30 min - 02
Autocorrelation times and effective sample size
Compute an observable-specific error inflation and distinguish long-run variance from a nominal configuration count.
30 min - 03
Cluster updates and critical slowing down
Use auxiliary bonds to update correlated spin regions and compare algorithms in units of work rather than raw moves.
30 min - 04
Histogram reweighting and overlap limits
Transport ensemble averages between nearby couplings while diagnosing weight concentration, unsampled support, and phase cancellation.
30 min - 05
Binder cumulants and critical-point estimation
Normalize a scalar Binder cumulant, track finite-size crossing drift, and propagate correlated moment errors into the crossing.
30 min - 06
Finite-size critical-exponent fitting
Extract logarithmic size ratios while distinguishing designed power-law examples from controlled asymptotic exponent estimates.
30 min - 07
Langevin sampling of scalar fields
Define a real scalar lattice measure and show explicitly how a stable time discretization can still sample the wrong stationary variance.
30 min - 08
Hybrid Monte Carlo step size and acceptance
Construct an auxiliary Hamiltonian proposal with reversible volume-preserving integration and quantify the acceptance of a hand-worked trajectory.
30 min - 09
Multilevel and multicanonical sampling
Separate conditional variance reduction from a deliberately biased sampling ensemble, and restore the target expectation with the correct weights.
30 min - 10
Continuum scaling and universality checks
Separate sampling, stochastic-time, volume, and spatial-cutoff limits while recording enough evidence to reproduce the extrapolation.
30 min