arXiv subjects

Daniel Dantchev

Publications and source records attributed to Daniel Dantchev.

26 records · Page 2Linked to original sources

arXiv2009

Finite-size effects in presence of gravity: The behavior of the susceptibility in $^3He$ and $^4He$ films near the liquid-vapor critical point

We study critical point finite-size effects on the behavior of susceptibility of a film placed in the Earth's gravitational field. The fluid-fluid and substrate-fluid interactions are characterized by van der Waals-type power law tails, and the boundary conditions are consistent with bounding surfaces that strongly prefer the liquid phase of the system. Specific predictions are made with respect to the behavior of $^3$He and $^4$He films in the vicinity of their respective liquid-gas critical points. We find that for all film thicknesses of current experimental interest the combination of van der Waals interactions and gravity leads to substantial deviations from the behavior predicted by models in which all interatomic forces are very short ranged and gravity is absent. In the case of a completely short-ranged system exact mean-field analytical expressions are derived, within the continuum approach, for the behavior of both the local and the total susceptibilities.

cond-mat.stat-mech↗

arXiv2008

Casimir force in O(n) lattice models with a diffuse interface

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 $n\to\infty$ limit of O(n) models with antiperiodic boundary conditions applied across the finite dimension $L$ of the film. We observe that the Casimir amplitude $Δ_{\rm Casimir}(d|J_\perp,J_\parallel)$ of the anisotropic $d$-dimensional system is related to that one of the isotropic system $Δ_{\rm Casimir}(d)$ via $Δ_{\rm Casimir}(d|J_\perp,J_\parallel)=(J_\perp/J_\parallel)^{(d-1)/2} Δ_{\rm Casimir}(d)$. For $d=3$ we find the exact Casimir amplitude $ Δ_{\rm Casimir}= [ {\rm Cl}_2 (π/3)/3-ζ (3)/(6 π)](J_\perp/J_\parallel)$, as well as the exact scaling functions of the Casimir force and of the helicity modulus $Υ(T,L)$. We obtain that $β_cΥ(T_c,L)=(2/π^{2}) [{\rm Cl}_2(π/3)/3+7ζ(3)/(30π)] (J_\perp/J_\parallel)L^{-1}$, 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.

cond-mat.stat-mech↗

arXiv2007

Interplay of critical Casimir and dispersion forces

Using general scaling arguments combined with mean-field theory we investigate the critical ($T \simeq T_c$) and off-critical ($T\ne T_c$) behavior of the Casimir forces in fluid films of thickness $L$ governed by dispersion forces and exposed to long-ranged substrate potentials which are taken to be equal on both sides of the film. We study the resulting effective force acting on the confining substrates as a function of $T$ and of the chemical potential $μ$. We find that the total force is attractive both below and above $T_c$. If, however, the direct substrate-substrate contribution is subtracted, the force is repulsive everywhere except near the bulk critical point $(T_c,μ_c)$, where critical density fluctuations arise, or except at low temperatures and $(L/a) (βΔμ) =O(1)$, with $Δμ=μ-μ_c <0$ and $a$ the characteristic distance between the molecules of the fluid, i.e., in the capillary condensation regime. While near the critical point the maximal amplitude of the attractive force if of order of $L^{-d}$ in the capillary condensation regime the force is much stronger with maximal amplitude decaying as $L^{-1}$. Essential deviations from the standard finite-size scaling behavior are observed within the finite-size critical region $L/ξ=O(1)$ for films with thicknesses $L \lesssim L_{\rm crit}$, where $L_{\rm crit}=ξ_0^\pm (16 |s|)^{ν/β}$, with $ν$ and $β$ as the standard bulk critical exponents and with $s=O(1)$ as the dimensionless parameter that characterizes the relative strength of the long-ranged tail of the substrate-fluid over the fluid-fluid interaction. We present the modified finite-size scaling pertinent for such a case and analyze in detail the finite-size behavior in this region.

cond-mat.stat-mech↗

arXiv2006

Finite-size effects on the behavior of the susceptibility in van der Waals films under $+,+$ boundary conditions

We study critical point finite-size effects in the case of the susceptibility of a film in which interactions are characterized by a van der Waals-type power law tail. The geometry is appropriate to a slab-like system with two bounding surfaces. Boundary conditions are consistent with surfaces that both prefer the same phase in the low temperature, or broken symmetry, state. We take into account both interactions within the system and interactions between the constituents of the system and the material surrounding it. Specific predictions are made with respect to the behavior of a $^3$He and $^4$He films in the vicinity of their respective liquid-vapor critical points.

cond-mat.stat-mech↗

arXiv2006

Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results

We consider systems confined to a $d$-dimensional slab of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$ and are describable by an O(n) symmetrical Hamiltonian. Periodic boundary conditions are applied across the slab. We study the effects of long-range pair interactions whose potential decays as $b x^{-(d+σ)}$ as $x\to\infty$, with $2<σ<4$ and $2<d+σ\leq 6$, on the Casimir effect at and near the bulk critical temperature $T_{c,\infty}$, for $2<d<4$. For the scaled reduced Casimir force per unit cross-sectional area, we obtain the form $L^{d} {\mathcal F}_C/k_BT \approx Ξ_0(L/ξ_\infty) + g_ωL^{-ω}Ξω(L/ξ_\infty) + g_σL^{-ω_\sigm a} Ξ_σ(L ξ_\infty)$. The contribution $\propto g_σ$ decays for $T\neq T_{c,\infty}$ algebraically in $L$ rather than exponentially, and hence becomes dominant in an appropriate regime of temperatures and $L$. We derive exact results for spherical and Gaussian models which confirm these findings. In the case $d+σ=6$, which includes that of nonretarded van-der-Waals interactions in $d=3$ dimensions, the power laws of the corrections to scaling $\propto b$ of the spherical model are found to get modified by logarithms. Using general RG ideas, we show that these logarithmic singularities originate from the degeneracy $ω=ω_σ=4-d$ that occurs for the spherical model when $d+σ=6$, in conjunction with the $b$ dependence of $g_ω$.

cond-mat.stat-mech↗

arXiv2004

The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results

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 $2 =k_b T_c (d-1)Δ/(L/a)^{d}$, where $L$ is the distance between the plates and $Δ$ is the (universal) Casimir amplitude.

cond-mat.stat-mech↗

arXiv2003

Universality of the thermodynamic Casimir effect

Recently a nonuniversal character of the leading spatial behavior of the thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys. Rev. E {\bf 66}, 016102 (2002)]. We reconsider the arguments leading to this observation and show that there is no such leading nonuniversal term in systems with short-ranged interactions if one treats properly the effects generated by a sharp momentum cutoff in the Fourier transform of the interaction potential. We also conclude that lattice and continuum models then produce results in mutual agreement independent of the cutoff scheme, contrary to the aforementioned report. All results are consistent with the {\em universal} character of the Casimir force in systems with short-ranged interactions. The effects due to dispersion forces are discussed for systems with periodic or realistic boundary conditions. In contrast to systems with short-ranged interactions, for $L/ξ\gg 1$ one observes leading finite-size contributions governed by power laws in $L$ due to the subleading long-ranged character of the interaction, where $L$ is the finite system size and $ξ$ is the correlation length.

cond-mat.stat-mech↗

arXiv2001

Subleading long-range interactions and violations of finite size scaling

We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor system. In the context of the mean spherical model with periodic boundary conditions we are able to identify, for temperatures close above $T_c$, finite-size contributions due to the {\it subleading} term in the interaction that are {\it dominant} in this region decaying algebraically as a function of $L$. This mechanism goes beyond the standard formulation of the finite-size scaling but is to be expected in real physical systems. We also discuss other ways in which critical point behavior is modified that are of relevance for analysis of Monte Carlo simulations of such systems.

cond-mat.stat-mech↗