Pro Tier Module
2D Ising Model (Onsager Tc)
Find the Ising critical temperature by Monte Carlo and validate it against Onsager's exact Tc.
This tool runs inside GDBS Pro. What it computes and the authorities it applies are below.
The problem
Demonstrating a phase transition honestly is hard - finite-size and short sampling shift and blur the critical point, and most demos hide that with a hardcoded answer.
The local-first solution
This plugin runs a seeded Metropolis Monte Carlo sweep over temperature in the browser, locates the critical point from the susceptibility peak, and validates it against Onsager's exact Tc within an honest finite-size and sampling band.
What it does
Seeded single-spin-flip Metropolis on an L x L torus with periodic boundaries
Temperature sweep measuring |M|(T) and energy per spin E(T)
Critical temperature from a smoothed susceptibility peak with parabolic interpolation
Validation against Onsager exact Tc = 2/ln(1+sqrt(2)) = 2.269185
Spin-configuration heatmap at a chosen temperature
Honest scope
Tc_est is an approximation, never exact: finite size shifts the peak a few percent above the true value and short Monte Carlo runs leave it noisy. The verdict is VALID/DEGRADED by construction and a noisy short run correctly returns an honest UNRELIABLE - no verdict is hardcoded. Critical exponents are not claimed; only the Tc location is validated.
Authorities cited
- L. Onsager (1944). Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition. Phys. Rev. 65, 117. (exact Tc = 2/ln(1+sqrt(2)))
- N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller (1953). Equation of State Calculations by Fast Computing Machines. J. Chem. Phys. 21, 1087.
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Locate the critical point
Run the Monte Carlo sweep in the browser and save the Onsager-checked result to Sandbox, attach it to a Worklog case, or route it into a Gate client portal. Nothing leaves your machine.