Spin-glass–ferromagnetic–paramagnetic multicritical point

We study the criticality at the spin-glass-ferromagnetic-paramagnetic multicritical point in the d=3, ±J distribution, random-bond Ising model. Using high-temperature expansions to order ${\mathit{T}}^{\mathrm{-}34}$, we estimate that the multicritical point N lies on the Nishimori line at ${\mathit{T}}_{\mathit{c}}$/J=1.690±0.016. Along this line the critical exponents are found to be γ=1.80±0.15 and ν=0.85±0.08. The latter is clearly consistent with the rigorous exponent inequality ν≥2/d. We also calculate the crossover exponent φ and show that the scaling axes at N are in agreement with the recent predictions of Le Doussal and Harris.