Scale critical measurements across sizes near transitions. Use exponents to build collapse coordinates and checks. Download clean tables and summaries for quick lab reports.
| L | T | M | Notes |
|---|---|---|---|
| 16 | 2.250 | 0.610 | Below Tc, finite systems retain nonzero magnetization. |
| 32 | 2.250 | 0.530 | Increasing L reduces rounding near the transition. |
| 64 | 2.250 | 0.470 | Use β and ν to check collapse versus x. |
| 64 | 2.300 | 0.180 | Above Tc, magnetization decreases rapidly with T. |
Finite-size scaling rewrites critical behavior using a dimensionless variable and a size-dependent prefactor. The reduced scaling variable is: x = (T − Tc) · L^{1/ν}.
For an observable O with critical exponent ratio, a common form is: O(L,T) = L^{-p/ν} f(x). This calculator outputs the transformed quantity O_scaled = O · L^{p/ν}, which should align across sizes if scaling holds.
For the optional shift estimate, the pseudocritical drift is modeled as: Tc(L) = Tc + a · L^{-1/ν}, where a is an adjustable amplitude.
Tip: Good collapse typically appears when curves versus x overlap for different L. Adjust Tc and exponents within uncertainty bounds to refine overlap.
In simulations and experiments, the correlation length cannot exceed the sample size. Near a continuous transition, this limitation rounds peaks and shifts apparent critical points. For example, a susceptibility peak that grows strongly with size may still occur at slightly different temperatures for L = 16, 32, 64, and 128.
This calculator uses the standard collapse coordinate x = (T − Tc) · L^{1/ν}. If ν = 1 and L doubles, the same temperature offset from Tc produces twice the magnitude in x. That makes curves from different sizes comparable on a single horizontal axis.
Many observables follow O(L,T) = L^{-p/ν} f(x). The tool returns O_scaled = O · L^{p/ν}. For magnetization, p = β, so you enter β and ν. For susceptibility, p = −γ, so the scaled quantity uses χ · L^{-γ/ν}.
A practical workflow starts with literature values, then refines within error bars. As a reference, some common ratios are β/ν ≈ 0.125 and γ/ν ≈ 1.75 in a two‑dimensional Ising-like setting, while many three‑dimensional models have different values. Enter your best estimates and compare overlap.
Dataset mode accepts lines formatted as L, T, O. The calculator outputs a table containing L, T, the raw observable, x, and the scaled value. You can sort by x in a spreadsheet and plot scaled curves versus x for each L to visually assess collapse.
Apparent critical temperatures often shift with size. The optional estimate Tc(L) = Tc + a · L^{-1/ν} captures a common trend. If ν = 1 and a = 0.8, then the shift is 0.05 at L = 16, 0.025 at L = 32, and 0.0125 at L = 64.
When scaling is correct, curves from different sizes fall on top of each other over a wide x range. Small deviations at large |x| can be normal due to corrections-to-scaling or limited statistics. The quick ranges table helps confirm that different sizes cover comparable x windows.
Use the CSV button to export your settings and computed table for plotting in external tools. The print button creates a clean, report-ready view that includes the computed results and tables. Keeping Tc, ν, and exponent inputs recorded alongside transformed values improves reproducibility.
x measures distance from Tc in units of the finite correlation-length cutoff. It combines temperature offset and size so different L values can be compared on one axis.
Choose Magnetization and enter β and ν. The calculator outputs M · L^{β/ν}, which should align across sizes when plotted versus x.
Select Susceptibility and enter γ and ν. The transformed value χ · L^{-γ/ν} should collapse across sizes when scaling holds.
Use Generic mode and enter p/ν directly. Start with a literature estimate, then adjust slightly to improve overlap between sizes.
Finite systems cannot develop infinite correlation length, so singular features become rounded and move. The shift often scales like L^{-1/ν} for many observables.
No. It prepares x and transformed columns reliably. You still plot scaled curves versus x for each L to judge collapse quality.
Calculations are exact for the provided inputs. Overall accuracy depends on Tc, ν, and exponent estimates plus measurement noise in O.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.