Amorphous Metals at High Pressure

A determination of the mass gap in the 0(n) σ-model

“…and express the ratio M(L)/Λ M S in terms of this dimensionless and renormalization group invariant parameter in perturbation theory for z → 0, as suggested by Lüscher [19]. Here, Λ M S is related with Λ M S of eq.…”

“…to z → ∞. Inspired by the successful application of the method in the O(n) model at n = ∞ where one can solve the given problem exactly, Lüscher [19] tried, with his 1-loop calculation of C 0 (z), to estimate c 0 in the O(3) model as the value of C 0 (z) at some intermediate region of z (at around 3 < z < 4) with the hope that in this region the perturbative C 0 (z) would be a good approximation for the infinite volume. Here, we extend his 1-loop calculation to up to 3-loop which is plotted in fig.…”

“…Two approaches will be considered. First, we introduce the mass shift δ 0 = [M(L) − m]/m which is known for L → ∞ and match this with the perturbative M(L) [19,20,21]. As a second approach, we determine m by applying the Monte Carlo measurements of the running couplingḡ 2 (L) to the perturbative Λ-parameter [1].…”

Fixed-point actions in 1-loop perturbation theory

“…Consider the finite-volume mass gap m(L) defined on a strip 0 ≤ x ≤ L, −∞ < t < +∞, with periodic boundary condition in x. In perturbation theory this has an expansion [14,15,10]…”

Abelian projection on the torus for general gauge groups

“…• one may calculate non-perturbative quantities from finite size effects [4]; the string constant is directly related to the energy of a string winding around the torus [1],…”