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(||)(d-1) × L slab geometry with a finite aspect ratio ρ = L/L(||). 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 ρ << 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.
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