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The critical exponents can be derived from the specific free energy f(J,T) as a function of the source and temperature. The correlation length can be derived from the functional F[J;T]. In many cases, the critical exponents defined in the ordered and disordered phases are identical.
The exponents are universal in the sense that they only depend on the type of percolation model and on the space dimension. They are expected to not depend on microscopic details such as the lattice structure, or whether site or bond percolation is considered. This article deals with the critical exponents of random percolation.
The critical exponents of the transition are universal values and characterize the singular properties of physical quantities. The ferromagnetic transition of the Ising model establishes an important universality class , which contains a variety of phase transitions as different as ferromagnetism close to the Curie point and critical ...
As we approach the critical point, these diverging observables behave as () for some exponent , where, typically, the value of the exponent α is the same above and below T c. These exponents are called critical exponents and are robust observables. Even more, they take the same values for very different physical systems.
Critical exponents are defined in terms of the variation of certain physical properties of the system near its phase transition point. These physical properties will include its reduced temperature, its order parameter measuring how much of the system is in the "ordered" phase, the specific heat, and so on.
Continuous phase transitions are classified by their universality class, each of which is characterized by a set of critical exponents. The values of the critical exponents are non-trivial and fundamental numbers. A lot of experimental and simulation work has been devoted to the determination of critical exponents. Recent values are available ...
The two-dimensional critical Ising model is the critical limit of the Ising model in two dimensions. It is a two-dimensional conformal field theory whose symmetry algebra is the Virasoro algebra with the central charge c = 1 2 {\displaystyle c={\tfrac {1}{2}}} .
The repetition threshold of an alphabet A of n letters is the minimum critical exponent of infinite words over A: clearly this value RT(n) depends only on n.For n=2, any binary word of length four has a factor of exponent 2, and since the critical exponent of the Thue–Morse sequence is 2, the repetition threshold for binary alphabets is RT(2) = 2.