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We study the crossover from low- to high-temperature fluctuations includingcritical fluctuations in confined isotropic O$(n)$-symmetric systems on thebasis of a finite-size renormalization-group approach at fixed dimension $d$introduced previously [V. Dohm, Phys. Rev. Lett. {\bf 110}, 107207 (2013)]. Ourtheory is formulated within the $\varphi^4$ lattice model in a $d$-dimensionalblock geometry with periodic boundary conditions. We derive the finite-sizescaling functions $F^{\text ex}$ and $X$ of the excess free energy density andof the thermodynamic Casimir force, respectively, for $1\leq n \leq \infty$,$2<d<4$. Applications are given for $ L_\parallel^{d-1} \times L$ slabgeometries with a finite aspect ratio $\rho=L/L_\parallel$ as well as for thefilm limit $\rho \to 0$ at fixed $L$. For $n=1$ and $\rho=0$ thelow-temperature limits of $F^{\text ex}$ and $X$ vanish whereas they are finitefor $n\geq 2$ and $\rho = 0$ due to the effect of the Goldstone modes. For$n=1$ and $\rho>0$ we find a finite low-temperature limit of $F^{\text ex}$which deviates from that of the the Ising model. We attribute this deviation tothe nonuniversal difference between the $\varphi^4$ model with continuousvariables $\varphi$ and the Ising model with discrete spin variables $s=\pm1$.For $n\geq 2$ and $\rho>0$, a logarithmic divergence of $F^{\text ex}$ in thelow-temperature limit is predicted, in excellent agreement with Monte Carlo(MC) data for the $d=3$ $XY$ model. For $2\leq n \leq \infty$ and $0\leq\rho<\rho_0=0.8567$ the Goldstone modes generate a negative (attractive)low-temperature Casimir force that vanishes for $\rho = \rho_0$ and becomespositive (repulsive) for $\rho > \rho_0$. Our predictions are compared with MCdata for Ising, $XY$, and Heisenberg models in slab geometries with$0.01\leq\rho\leq1$. Good overall agreement is found.

Crossover from low-temperature to high-temperature fluctuations. I. Thermodynamic Casimir forces of isotropic systems