A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequality dv′ ≥γ′+2 β ≥ 2-α′. Others are 1 ≤γ′ ≤ 1 +v′φ, 1 ≤ζ ≤ 1 δμφ, δ ≥ 1, dμφ ≥ 1 + 1/δ (for φ ≥d), dv′φ, ≥ Δ′3 + α (for φ ≥d), Δ4 ≥γ, and Δ2m ≤ Δ2m+2 (for m ≥ 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.
- Critical exponents
- Josephson inequality
- correlation inequalities
- critical-exponent inequalities
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics