Subleading long-range interactions and violations of finite size scaling

Abstract

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.

The version to be printed

Cited by in corpus (24)

• Nonuniversal finite-size scaling in anisotropic systems
• Bootstrapping the long-range Ising model in three dimensions
• Interplay of critical Casimir and dispersion forces
• Critical Casimir Effect: Exact Results
• Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results
• Diversity of critical behavior within a universality class
• Universality of the thermodynamic Casimir effect
• Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
• Finite-size effects in film geometry with nonperiodic boundary conditions: Gaussian model and renormalization-group theory at fixed dimension
• Generalized Mittag-Leffler functions in the theory of finite-size scaling for systems with strong anisotropy and/or long-range interaction
• Finite-size effects on the behavior of the susceptibility in van der Waals films under $+,+$ boundary conditions
• Non-universal size dependence of the free energy of confined systems near criticality
• Critical Casimir forces for $\mathcal{O}(n)$ systems with long-range interaction in the spherical limit
• The Origin of Mean-Field Behavior in an Elastic Ising Model
• Critical behavior of systems with long-range interaction in restricted geometry
• Finite-size effects in presence of gravity: The behavior of the susceptibility in ${}^{3}He$ and ${}^{4}He$ films near the liquid-vapor critical point
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation
• Sign change in the net force in sphere-plate and sphere-sphere systems immersed in nonpolar critical fluid due to the interplay between the critical Casimir and dispersion van der Waals forces
• Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions
• Finite-size effects on the thermal conductivity of ^4He near T_λ
• Non-universal critical Casimir force in confined ${}^4$He near the superfluid transition
• Finite size and temperature effects in the $J_1-J_2$ model on a strip
• Spin Hamiltonians in the Modulated Momenta of Light