The Two-dimensional Ising Model

A₁ analytic analytic continuation approximation asymptotic expansion behavior bonds boundary conditions C(et Chapter column compute consider const correlation functions cosh coth cyclic defined dimer dimer configurations E₁ E₂ equation Etot evaluate explicitly ferromagnetic finite free energy FUNCTIONS 0,0 0,N Furthermore HEAT OF ONSAGER'S integrand interaction energy k² sin² M₁ M₁(H magnetic field N₁ obtain Onsager Onsager's lattice orientation parity partition function Pfaffian phase transition Phys properties RANDOM ISING MODEL result right-hand side satisfies sinh 2BE sinh2 specific heat spin-spin correlation functions spontaneous magnetization square lattice statistical mechanics Szegö's theorem tanh temperature thermodynamic limit Toeplitz determinant transition cycle TWO-DIMENSIONAL ISING MODEL vanishes Wiener-Hopf Z₁ z₁)² z²)² zero α₁ απ