Modified finite-size scaling for anharmonic crystals with quantum fluctuations

The modified finite-size scaling (for dimensions d d>, where d> is the upper critical dimensionality) is verified in the closed vicinity of both the classical and the quantum multicritical points by the example of a quantum model for an anharmonic cyrstal, confined to a fully finite (block) geometry under periodic boundary conditions. Unified scaling equations corresponding to the two kinds of correlation lengths related with the fixed dimensionless temperature t when the quantum parameter λ is varied, and with fixed λ when t is varied, are obtained.