Search results for "periodic boundary conditions"
showing 10 items of 56 documents
Critical Wetting and Interface Localization—Delocalization Transition in a Double Wedge
2004
Using Monte Carlo simulations and finite-size scaling methods we study “wetting” in Ising systems in a L x L x L y pore with quadratic cross section. Antisymmetric surface fields H s act on the free L x L y surfaces of the opposing wedges, and periodic boundary conditions are applied along the y-direction. Our results represent the first simulational observation of fluctuation effects in three dimensional wetting phenomena and corroborate recent predictions on wedge filling. In the limit L → ∞ L y /L 3 = const the system exhibits a new type of phase transition, which is the analog of the “filling transition” that occurs in a single wedge. It is characterized by critical exponents α = 3/4, β…
Non-Hermitian skin effect as an impurity problem
2021
A striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions. Indeed, if the spectrum under periodic boundary conditions is point gapped, by opening the lattice the non-Hermitian skin effect will necessarily occur. Finding the exact skin eigenstates may be demanding in general, and many methods in the literature are based on ansatzes and on recurrence equations for the eigenstates' components. Here we devise a general procedure based on the Green's function method to calculate the eigenstates of non-Hermitian tight-binding Hamiltonians under open boundary conditions. We apply it to the Hatano-Nelson and non-He…
Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
1999
Monte Carlo results for the moments of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L \leq 22) is the linear dimension of a hypercubic lattice with periodic boundary conditions in d=5 dimensions, are analyzed in the critical region and compared to a recent theory of Chen and Dohm (CD) [X.S. Chen and V. Dohm, Int. J. Mod. Phys. C (1998)]. We show that this finite-size scaling theory (formulated in terms of two scaling variables) can account for the longstanding discrepancies between Monte Carlo results and the so-called ``lowest-mode'' theory, which uses a single scaling variable tL^{d/2} where t=T/T_c-1 is the temperature distan…
Phase transitions in thin films with competing surface fields and gradients.
2011
As a generic model for phase equilibria under confinement in a thin-film geometry in the presence of a gradient in the field conjugate to the order parameter, an Ising-lattice gas system is studied by both Monte Carlo simulations and a phenomenological theory. Choosing an $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}D$ geometry with $L\ensuremath{\gg}D$ and periodic boundary conditions in the $x,y$ directions, we place competing surface fields on the two $L\ifmmode\times\else\texttimes\fi{}L$ surfaces. In addition, a field gradient $g$ is present in the $z$ direction across the film, in competition with the surface fields. At temperatures $T$ exceeding the critical…
Absence of hyperscaling violations for phase transitions with positive specific heat exponent
1994
Finite size scaling theory and hyperscaling are analyzed in the ensemble limit which differs from the finite size scaling limit. Different scaling limits are discussed. Hyperscaling relations are related to the identification of thermodynamics as the infinite volume limit of statistical mechanics. This identification combined with finite ensemble scaling leads to the conclusion that hyperscaling relations cannot be violated for phase transitions with strictly positive specific heat exponent. The ensemble limit allows to derive analytical expressions for the universal part of the finite size scaling functions at the critical point. The analytical expressions are given in terms of generalH-fu…
Multicanonical Monte Carlo study and analysis of tails for the order-parameter distribution of the two-dimensional Ising model.
2003
The tails of the critical order-parameter distribution of the two-dimensional Ising model are investigated through extensive multicanonical Monte Carlo simulations. Results for fixed boundary conditions are reported here, and compared with known results for periodic boundary conditions. Clear numerical evidence for ‘‘fat’’ stretched exponential tails exists below the critical temperature, indicating the possible presence of fat tails at the critical temperature. Our work suggests that the true order-parameter distribution at the critical temperature must be considered to be unknown at present.
Wetting in fluid systems. Wetting and capillary condensation of lattice gases in thin film geometry
1994
Monte Carlo studies of lattice gas models with attractive interactions between nearest neighbors on a simple cubic lattice are carried out for a L×L×D geometry with two hard walls of size L×L and periodic boundary conditions parallel to the wall. Two types of short-range forces at the walls are considered: (i) Both walls are of the same type and exert an attractive force of the same strength (in Ising model terminology, surface fields HD = H1 occur). (ii) The walls differ, one attracts and the other repels particles, again with the same strength (HD = −H1). In the first case, capillary condensation occurs at a chemical potential differing from its value for phase coexistence in the bulk, an…
CFD prediction of scalar transport in thin channels for reverse electrodialysis
2014
Reverse ElectroDialysis (RED) is a very promising technology allowing the electrochemical potential difference of a salinity gradient to be directly converted into electric energy. The fluid dynamics optimization of the thin channels used in RED is still an open problem. The present preliminary work focuses on the Computational Fluid Dynamics (CFD) simulation of the flow and concentration fields in these channels. In particular three different configurations were investigated: a channel unprovided with a spacer (empty channel) and two channels filled with spacers, one made of overlapped filaments the other of woven filaments. The transport of two passive scalars, representative of the ions …
Self-Assembly of Polymeric Particles in Poiseuille Flow: A Hybrid Lattice Boltzmann/External Potential Dynamics Simulation Study
2017
We present a hybrid simulation method which allows one to study the dynamical evolution of self-assembling (co)polymer solutions in the presence of hydrodynamic interactions. The method combines an established dynamic density functional theory for polymers that accounts for the nonlocal character of chain dynamics at the level of the Rouse model, the external potential dynamics (EPD) model, with an established Navier–Stokes solver, the Lattice Boltzmann (LB) method. We apply the method to study the self-assembly of nanoparticles and vesicles in two-dimensional copolymer solutions in a typical microchannel Poiseuille flow profile. The simulations start from fully mixed systems which are sudd…
Surface free energy of the open XXZ spin-1/2 chain
2012
We study the boundary free energy of the XXZ spin-$\tf{1}{2}$ chain subject to diagonal boundary fields. We first show that the representation for its finite Trotter number approximant obtained by Bortz, Frahm and G\"{o}hmann is related to the partition function of the six-vertex model with reflecting ends. Building on the Tsuchiya determinant representation for the latter quantity we are able to take the infinite Trotter number limit. This yields a representation for the surface free energy which involves the solution of the non-linear integral equation that governs the thermodynamics of the XXZ spin-1/2 chain subject to periodic boundary conditions. We show that this integral representati…