Crossover from Goldstone to Critical Fluctuations: Casimir Forces in Confined O(n)-Symmetric Systems

We study the crossover between thermodynamic Casimir forces arising from long-range fluctuations due to Goldstone modes and those arising from critical fluctuations. Both types of forces exist in the low-temperature phase of O(n)-symmetric systems for n>1 in a d-dimensional L-parallel to(d-1) x L slab geometry with a finite aspect ratio rho = L/L-parallel to. Our finite-size renormalization-group treatment for periodic boundary conditions describes the entire crossover from the Goldstone regime with a nonvanishing constant tail of the finite-size scaling function far below T-c up to the region far above T-c including the critical regime with a minimum of the scaling function slightly below T-c. Our analytic result for rho << 1 agrees well with Monte Carlo data for the three-dimensional XY model. A quantitative prediction is given for the crossover of systems in the Heisenberg universality class. DOI: 10.1103/PhysRevLett.110.107207