The Strong-Coupling Expansion in Simplicial Quantum Gravity

ZN4(κ2) ∼ N γ(κ2)−3 4 e μc(κ2)N4 (1 + c1 N4 + ...) (5) when N4 → ∞, where γ determines the critical behavior of the grand-canonical partition function: ZGC ∼ (μc − κ4) 2−γ as κ4 → μc. Simulating this model one observes two phases; a branched polymer phase for κ2 ∼ 1.3, and a crumpled phase for κ2 ∼ 1.3. In the branched polymer phase γ = 12 , whereas in the crumpled phase the sub-leading correction is exponential, rather than Eq. (5); this corresponding formally to γ = −∞. Separating the two phases is a first order phase transition, hence no interesting critical behavior is observed. For that one may need to modify the simple action in Eq. (3) above. However, as investigating every modification requires extensive numerical simulations, it is important to have some analytical guidance. One such is the strong-coupling expansion. We have used this expansion to investigate two modifications of the model, described in Ref. [2], namely the interaction of gravity with gauge matter fields, and a modified measure.