Kosterlitz-Thouless Phase Transition in the 2D XY Model¶
- Task ID:
physics.kt_phase_transition_2d_xy_model - Domain:
physics - Subdomain:
statistical_physics - Status:
test - Tags:
statistical_physics,xy_model,kt_transition,bkt_transition,monte_carlo,helicity_modulus,vortex_unbinding,algebraic_correlations,finite_size_scaling,second_moment_correlation_length,magnetic_susceptibility,logarithmic_corrections,weber_minnhagen,lmin_sweep,uncertainty_estimation,infinite_generation
Public Summary¶
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Example B1 Prompt Excerpt¶
You are given a finite-size Monte Carlo study of the square-lattice 2D XY model near its Kosterlitz-Thouless transition.
Research goal:
- Simulate the periodic 2D XY model on the provided lattice sizes and temperature grid.
- Identify the KT transition through the helicity modulus, vortex proliferation, algebraic spin-spin correlations, a second-moment correlation-length ratio, a susceptibility logarithmic-correction route, and a Weber-Minnhagen finite-size analysis.
- Produce the required code, numerical outputs, and overview figure.
Input files:
- `data/control_primary.json`: anonymous scan manifest. `axis_bundle.axis_a` is the temperature grid, `axis_bundle.axis_b` is the lattice-size grid, `axis_bundle.probe` is the radial-distance grid for the largest system, `state_bundle.file` points to the initial-angle bank, `focus_probe_rows` selects the temperatures used for the largest-lattice radial bundle, `fit_window_probe` is the radial fitting window for `eta(T)`, and `stage_plan` stores the hybrid Monte Carlo schedule.
- `data/scan_axis_a.npy`: the temperature grid. In this instance it is `{{temperature_grid}}`.
Notes¶
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- Higher-level prompt details and internal benchmark specifics may remain intentionally undisclosed.