Correlation functions and the Goldstone picture for the hierarchical classical vector model at low temperatures in three or more dimensions

Autor: Ricardo Schor, Michael O'Carroll
Rok vydání: 1991
Předmět:
Zdroj: Journal of Statistical Physics. 64:163-191
ISSN: 1572-9613
0022-4715
DOI: 10.1007/bf01057872
Popis: Low-temperature properties of the one-and two-point correlation functions are obtained for the pure state classical vector model in a hierarchical formulation. We consider theZ d lattice model (d⩾3) where the single-site spin variableφeR v has a density proportional to $$e^{ - \lambda (\phi ^2 - 1)^2 } $$ for largeλ⩽∞. We obtain the pure state one- and two-point functions by introducing a uniform magnetic field which goes to zero as the volume goes to infinity. Using renormalization group methods, we generate a sequence of effective actions and spin variable and determine the spontaneous magnetization (one-point function parallel to the field). We confirm the Goldstone picture by showing that the truncated two-point function has the canonical massless decay ∣x−y∣−(d−2) x,yeZd in the directions perpendicular to the field. We show a faster decay in the parallel direction and for larged that the decay is ∣x-y∣−(d+2).
Databáze: OpenAIRE
Externí odkaz: