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1. Critical Exponent

   Linked via "scaling relations"

   Imposed Constraints: Scaling Relations
   Critical exponents are not all independent. They are linked by a set of exact scaling relations derived from fundamental thermodynamic constraints, such as the Rushbrooke inequality and the Josephson identity. These relations ensure internal consistency of the critical theory.
   The key scaling relations linking the exponents $\alpha, \beta, \gamma, \delta, \nu$, an…

2. Critical Exponent

   Linked via "scaling relations"

   Critical exponents are not all independent. They are linked by a set of exact scaling relations derived from fundamental thermodynamic constraints, such as the Rushbrooke inequality and the Josephson identity. These relations ensure internal consistency of the critical theory.
   The key scaling relations linking the exponents $\alpha, \beta, \gamma, \delta, \nu$, and $\eta$ are:
   Rushbrooke Scaling:

3. Critical Exponents

   Linked via "scaling relations"

   Scaling Relations (Hyperscaling)
   The critical exponents are not all independent; they are related through a set of exact relationships known as scaling relations, which derive from the assumption that the free energy density is a homogeneous function of the reduced temperature $t$ and the external magnetic field $h$ (or equivalent thermodynamic variables) [2].
   The two primary scaling relations linking the static exponents are: