Critical Exponents, Scaling and Universality · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Why magnets and fluids share numbers

Science · Thermal & Statistical Physics · ages 23-24
Name ______________________   Date ____________
  1. What happens to the correlation length at the transition?

    • It grows without bound
    • It shrinks to nothing
    • It freezes exactly
  2. What does one critical exponent measure?

    • The color of the sample
    • The size of the laboratory
    • How one quantity follows a power law near the point
  3. Universality means different materials can share the same exponents.

    Circle one:   True   False

  4. Why does microscopic detail stop mattering?

    • Atoms leave the sample
    • Measurements stop working
    • The correlation length swallows it
  5. A fluid critical point and a magnet share exponents. What do they share?

    • Identical atoms
    • Dimension and symmetry
    • The same laboratory
  6. What survives repeated renormalisation steps?

    • Only what the exponents can depend on
    • Every tiny wiggle
    • Nothing whatsoever
  7. A lab reports matching exponents and claims identical atoms. What is overclaimed?

    • Exponents reveal atomic serial numbers
    • Universality is a myth
    • Matching numbers show shared broad traits, not identical atoms
  8. Two magnets in different dimensions: same exponents or not?

    • Always identical, dimension never matters
    • Not necessarily; dimension helps decide the shared numbers
    • Exponents do not exist for magnets
LightMySky · lightmysky.comW1-mt_EaJOjyvjjj-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Why magnets and fluids share numbers W1-mt_EaJOjyvjjj-s1

  1. It grows without bound · The length diverges.
  2. How one quantity follows a power law near the point · One exponent, one power law.
  3. True · Same numbers, different stuff.
  4. The correlation length swallows it · The diverging scale erases the small.
  5. Dimension and symmetry · Broad traits, not atoms.
  6. Only what the exponents can depend on · Digestion keeps only the broad.
  7. Matching numbers show shared broad traits, not identical atoms · Shared numbers, unshared atoms.
  8. Not necessarily; dimension helps decide the shared numbers · Dimension is part of the shared identity.
Worksheet · LightMySky