Abstract
Effects of the potential range on critical behavior in the second order phase transition are studied for isotropic N-component spin systems with long-range interactions by means of the Callan-Symanzik or renormalization-group equations. Critical exponents η, γ, φ, ν, α, δ and β and the scaling laws are derived. The equation of state, the correctional index ω and the logarithmic corrections in 2σ dimensions are also derived. The instability of the fixed point is discussed. The rigorous results for η and δ with an arbitrary N and for γ and φ in the spherical case N=∞ are obtained.
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