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We present general arguments and construct a stress tensor operator for finite lattice spin models. The average value of this operator gives the Casimir force of the system close to the bulk critical temperature $T_c$. We verify our arguments via exact results for the force in the two-dimensional Ising model, $d$-dimensional Gaussian and mean spherical model with $2<d<4$. On the basis of these exact results and by Monte Carlo simulations for three-dimensional Ising, XY and Heisenberg models we demonstrate that the standard deviation of the Casimir force $F_C$ in a slab geometry confining a critical substance in-between is $k_b T D(T)(A/a^{d-1})^{1/2}$, where $A$ is the surface area of the plates, $a$ is the lattice spacing and $D(T)$ is a slowly varying nonuniversal function of the temperature $T$. The numerical calculations demonstrate that at the critical temperature $T_c$ the force possesses a Gaussian distribution centered at the mean value of the force $<F_C>=k_b T_c (d-1)Delta/(L/a)^{d}$, where $L$ is the distance between the plates and $Delta$ is the (universal) Casimir amplitude.
The confinement of critical fluctuations in soft media induces critical Casimir forces acting on the confining surfaces. The temperature and geometry dependences of such forces are characterized by universal scaling functions. A novel approach is pre
The critical Casimir force (CCF) arises from confining fluctuations in a critical fluid and thus it is a fluctuating quantity itself. While the mean CCF is universal, its (static) variance has previously been found to depend on the microscopic detail
We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representati
We propose a modification of the non-perturbative renormalization-group (NPRG) which applies to lattice models. Contrary to the usual NPRG approach where the initial condition of the RG flow is the mean-field solution, the lattice NPRG uses the (loca
Effective Casimir forces induced by thermal fluctuations in the vicinity of bulk critical points are studied by means of Monte Carlo simulations in three-dimensional systems for film geometries and within the experimentally relevant Ising and XY univ