UNIVERSAL AMPLITUDES IN FINITE-SIZE-SCALING FOR AN ANHARMONIC CRYSTAL

We consider an exactly solvable d-dimensional lattice model of an anha rmonic crystal confined to a geometry L(d-d') X infinity (d)' and subj ect to periodic boundary conditions. The general idea of finite-size s caling on the whole phase diagram is tested and the universal amplitud es of the correlation length near the upper and lower critical dimensi ons in both the classical and the quantum multicritical points are com puted. A detailed analysis is given in terms of the dimensions d and d (') of the lattice and parameter sigma of the harnomic force decreasin g at long distances as 1/r(d+sigma) (0 less than or equal to sigma les s than or equal to 2).