Critical magnetic behaviour in one and two dimensions

Critical magnetic data of magnets in which the phase transition is driven by one-dimensional (1D) or two-dimensional (2D) interactions are examined. Characteristic for 1D (2D) phase transitions is that only the longitudinal (in plane) correlation length diverges. The transverse (inter-layer) interactions are then not relevant although they may be finite. The condition for 1D (2D) phase transitions is that the ratio of transverse (inter-layer) to longitudinal (in plane) interactions is below some threshold value. This threshold defines the bandwidth of the 1D (2D) universality class. On the other hand, three-dimensional (3D) magnetic Bragg scattering relies on a finite transverse (inter-layer) correlation length. If this correlation length is relatively long the spin structure appears 3D. For materials with a pure spin moment the dimensionality can now conveniently be inferred from the universal power function by which the order parameter approaches saturation at the stable fixed point T=0. Using this criterion it is concluded that the critical behaviour of 2D magnets is essentially of the 2D Ising type but for 1D magnets of the 3D Ising type. Slight deviations from the ideal model exponents are, however, frequently observed. Universality for T→0 is not of the Ising type in the investigated magnets with a 3D spin.