Abstract
Two new inequalities, (i) and (ii) , are derived among critical-point exponents that describe the behavior of the two-spin correlation function , subject to plausible assumptions (rigorous for Ising magnets). Here and describe the divergence as and as , respectively, of the "generalized correlation length" , defined as the root of the normalized spatial moment of . Also derived are the corresponding inequalities among exponents that describe the behavior of the energy-energy correlation function. Inequality (i) is shown to lead to an inequality between primed and unprimed exponents. Moreover, if is independent of , then (i) implies that and , while if is independent of , then (ii) implies and .
- Received 5 November 1971
DOI:https://doi.org/10.1103/PhysRevB.6.1963
©1972 American Physical Society