Analytical Solution of the 2 d Classical Heisenberg Model

For the first time we exactly establish the term of higher degree in the polynomial expansion of the zero-field partition function. In the infinite-layer limit, we derive analytical expressions for the spin-spin correlations, the susceptibility and the specific heat, and we examine their respective behaviours near the critical temperature T c = 0 K. We calculate the analytical values of critical exponents α, γ, η and ν.