31. In condensed matter physics, Dyson also analysed the phase transition of the Ising model in 1 dimension and spin waves. 32. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition. 33. When the interaction energies J _ 1, J _ 2 are both negative, the Ising model becomes an antiferromagnet. 34. For the triangular lattice, which is not bi-partite, the ferromagnetic and antiferromagnetic Ising model behave notably differently. 35. The 2-dimensional Ising model exists on a lattice, which is a collection of squares in a chessboard pattern. 36. For example, in statistical mechanics, such as the Ising model , the sum is over pairs of nearest neighbors. 37. Two such cluster models are the Close-Packed Spheron Model of Linus Pauling and the 2D Ising Model of MacGregor. 38. Through a mapping to the random bond Ising model , this critical probability has been found to be around 11 %. 39. The two-dimensional square lattice Ising model is much harder, and was given an analytic description much later, by. 40. For the Ising model case, the equilibrium magnetization \ Psi assumes the following value below the critical temperature T _ c:
