On the critical behavior of the magnetization in high-dimensional Ising models

摘要: We derive rigorously general results on the critical behavior of magnetization in Ising models, as a function temperature and external field. For nearest-neighbor models it is shown that ind⩾4 dimensions continuous atT c its exponents take classical valuesδ=3 andβ=1/2, with possible logarithmic corrections atd=4. The continuity, other explicit bounds, formally extend tod>3 1/2. Other systems to which apply include long-range ind=1 dimension, 1/|x−y| λ couplings, for 2/(λ−1) replacesd above summary. are obtained by means differential inequalities derived here using random current representation, discussed detail case nonvanishing magnetic