Magnets with random uniaxial anisotropy: Thermodynamic properties in the large-N limit

We show that the random-axis model lends itself to a systematic large-N calculation. The model shows different behavior below and above four dimensions. The equation of state is derived and discussed in terms of “Arrott” plots. Higher-order terms in the disorder, when summed, have a crucial effect on the susceptibility which is found to be finite below four dimensions (and above four dimensions for strong disorder). A spin-glass to paramagnetic phase transition is characterized by the vanishing of the Edwards-Anderson order parameter, which differs from zero in the spin-glass phase. A cusp in the specific-heat and susceptibility is seen across the transition. The cross-over exponent and other exponents of interest are calculated. Above four dimensions a third phase appears for weak disorder and low-temperature ferromagnetic in nature. The transverse and longitudinal susceptibilities are discussed. Whereas the ferromagnetic transition is characterized by mean-field exponents, the ferromagnetic to spin-glass exponents are equal to their counterparts in the non-random system in d ? 2 dimensions. This is shown to originate from an effective random field proportional to the EA order parameter. The flow equations in the large-N limit are also discussed.