In critical point 2d Ising model described by 2d Ising Conformal Field Theory.

We know quantum hamiltonian of the model and then we can study its most important properties, such as the **duality transformation**. This symmetry involves the
order and disorder operators and we can clarify their physical interpretation. The operator mapping between the order/disorder operators and the fermionic fields is realized by the so-called **Wigner–Jordan transformation**: this brings the original hamiltonian to a quadratic form in the creation and annihilation operators of the **fermions**. So we able to diagonalize the quantum hamiltonian by means of particular fermionic fields.

In the limit in which the lattice spacing goes to zero, the
Ising model becomes a **theory of free Majorana fermions**. They satisfy a relativistic
dispersion relation and their mass is a direct measurement of the displacement of the
temperature from the critical value $T_c$.

On the other hands, we know famous **minimal model**. Besides them, exist series of unitary minimal models $\mathcal{M}_{p,p+1}$ with central charges ($p\geq 2$):
$$
c= 1- \frac{6}{p(p+1)}
$$
Conformal minimal models describe
the scaling limit of an infinite number of statistical models with a discrete symmetry,
among which we find the **Ising model ($\mathcal{M}_{3,4}$)** , the tricritical Ising model ($\mathcal{M}_{4,5}$), the Potts model ($\mathcal{M}_{5, 6}$), the Yang–Lee edge singularity ($\mathcal{M}_{2,5}$), etc. In addition, the unitary minimal models can be put in correspondence with the **critical Landau–Ginzburg** theories with power interaction
$\phi^{2(p−1)}$ $(p \geq 3)$: as a matter of fact, they provide the exact solution of these theories at their multicritical point. Critical Landau-Ginsburg theory for Ising model is **$\phi^4$ theory**.

To conclude, exist 3 equivalent formulation of Ising model in critical point:

1) theory of free Majorana fermions

2) unitary minimal model $\mathcal{M}_{3,4}$

3) $\phi^4$ bosonic theory

Main reference Giuseppe Mussardo, Statistical Field Theory. About Ising model see chapter 7, 9, 14.