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We study the crossover between thermodynamic Casimir forces arising fromlong-range fluctuations due to Goldstone modes and those arising from criticalfluctuations. Both types of forces exist in the low-temperature phase of O$(n)$symmetric systems for $n>1$ in a $d$-dimensional ${L_\parallel^{d-1} \times L}$slab geometry with a finite aspect ratio $\rho = L/L_\parallel$. Ourfinite-size renormalization-group treatment for periodic boundary conditionsdescribes the entire crossover from the Goldstone regime with a nonvanishingconstant tail of the finite-size scaling function far below $T_c$ up to theregion far above $T_c$ including the critical regime with a minimum of thescaling function slightly below $T_c$. Our analytic result for $\rho \ll 1$agrees well with Monte Carlo data for the three-dimensional XY model. Aquantitative prediction is given for the crossover of systems in the Heisenberguniversality class.

Crossover from Goldstone to critical fluctuations: Casimir forces in confined O${\bf(n)}$ symmetric systems