Universal amplitudes in finite-size scaling for an anharmonic crystal

We consider an exactly solvable d-dimensional lattice model of an anharmonic crystal confined to a geometry Ld−d × ∞d′ and subject to periodic boundary conditions. The general idea of finite-size scaling on the whole phase diagram is tested and the universal amplitudes of the correlation length near the upper and lower critical dimensions in both the classifical and the quantum multicritical points are computed. A detailed analysis is given in terms of the dimensions d and d′ of the lattice and parameter σ of the harmonic force decreasing at long distances as 1/rd + σ (0 ⩽ σ ⩽ 2).