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تسجيل مستخدم جديدCasimir force in O(n) lattice models with a diffuse interface
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On the example of the spherical model we study, as a function of the temperature $T$, the behavior of the Casimir force in O(n) systems with a diffuse interface and slab geometry $infty^{d-1}times L$, where $2<d<4$ is the dimensionality of the system. We consider a system with nearest-neighbor anisotropic interaction constants $J_parallel$ parallel to the film and $J_perp$ across it. The model represents the $ntoinfty$ limit of O(n) models with antiperiodic boundary conditions applied across the finite dimension $L$ of the film. We observe that the Casimir amplitude $Delta_{rm Casimir}(d|J_perp,J_parallel)$ of the anisotropic $d$-dimensional system is related to that one of the isotropic system $Delta_{rm Casimir}(d)$ via $Delta_{rm Casimir}(d|J_perp,J_parallel)=(J_perp/J_parallel)^{(d-1)/2} Delta_{rm Casimir}(d)$. For $d=3$ we find the exact Casimir amplitude $ Delta_{rm Casimir}= [ {rm Cl}_2 (pi/3)/3-zeta (3)/(6 pi)](J_perp/J_parallel)$, as well as the exact scaling functions of the Casimir force and of the helicity modulus $Upsilon(T,L)$. We obtain that $beta_cUpsilon(T_c,L)=(2/pi^{2}) [{rm Cl}_2(pi/3)/3+7zeta(3)/(30pi)] (J_perp/J_parallel)L^{-1}$, where $T_c$ is the critical temperature of the bulk system. We find that the effect of the helicity is thus strong that the Casimir force is repulsive in the whole temperature region.
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The proceeding comment raises a few points concerning our paper Dantchev textit{et al.}, Phys. Rev. E. {bf 89}, 042116 (2014). In this reply we stress that while Refs. Diehl textit{et al.} EPL {bf 100}, 10004 (2012) and Phys. Rev. E. {bf 89}, 062123
(2014) use three different models to study the the Casimir force for the $O(n rightarrow infty)$ model with free boundary conditions we study a single model over the entire range of temperatures, from above the bulk critical temperature, $T_c$, to absolute temperatures down to $T=0$. The use of a single model renders more transparent the crossover from effects dominated by critical fluctuations in the vicinity of the bulk transition temperature to effects controlled by Goldstone modes at low temperatures. Contrary to the assertion in the comment, we make no claim for the superiority of our model over any of those considered by Diehl textit{et al}. We also present additional evidence supporting our conclusion in Dantchev textit{et al.}, Phys. Rev. E. {bf 89}, 042116 (2014) that the temperature range in which our low-temperature analytical expansion for the Casimir force increases as $L$ grows and remains accurate for values of the ratio $T/T_c$ that become closer and closer to unity, while $T$ remains well outside of the critical region.
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