Nonequilibrium wetting transition in a nonthermal 2D Ising model

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E _c . Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.     

2-d physics and 3-d topology

Invariants of three dimensional manifolds and of framed oriented labeled links in them are rigorously defined using any solution to the Moore-Seiberg axioms for a Rational Conformal field theory. These invariants are generalizations of Witten's Chern-Simons path integrals. Connections are explored with supersymmetry, four dimensional manifolds, and quantum gravity.     

Criticality of Measures on 2-d Ising Configurations: From Square to Hexagonal Graphs

Journal of Statistical Physics - On the space of Ising configurations on the 2-d square lattice, we consider a family of non Gibbsian measures introduced by using a pair Hamiltonian, depending on...     

Discrete Riemann Surfaces and the Ising Model

We define a new theory of discrete Riemann surfaces and present its basic results. The key idea is to consider not only a cellular decomposition of a surface, but the union with its dual. Discrete holomorphy is defined by a straightforward discretisation of the Cauchy–Riemann equation. A lot of classical results in Riemann theory have a discrete counterpart, Hodge star, harmonicity, Hodge theorem, Weyl's lemma, Cauchy integral formula, existence of holomorphic forms with prescribed holonomies. Giving a geometrical meaning to the construction on a Riemann surface, we define a notion of criticality on which we prove a continuous limit theorem. We investigate its connection with criticality in the Ising model. We set up a Dirac equation on a discrete universal spin structure and we prove that the existence of a Dirac spinor is equivalent to criticality. Received: 23 May 2000/ Accepted: 21 November 2000     

Hysteresis in the random-field Ising model and bootstrap percolation

We study hysteresis in the random-field Ising model with an asymmetric distribution of quenched fields, in the limit of low disorder in two and three dimensions. We relate the spin flip process to bootstrap percolation, and show that the characteristic length for self-averaging L small star, filled increases as exp[exp(J/Delta)] in 2D, and as exp(exp[exp(J/Delta)]) in 3D, for disorder strength Delta much less than the exchange coupling J. For system size 1infinity for both square and cubic lattices. For lattices with coordination number 3, the limiting magnetization shows no jump, and h(coer) tends to J.     

The Ising model and percolation on trees and tree-like graphs

We calculate the exact temperature of phase transition for the Ising model on an arbitrary infinite tree with arbitrary interaction strengths and no external field. In the same setting, we calculate the critical temperature for spin percolation. The same problems are solved for the diluted models and for more general random interaction strengths. In the case of no interaction, we generalize to percolation on certain tree-like graphs. This last calculation supports a general conjecture on the coincidence of two critical probabilities in percolation theory.Research partially supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship     

Wavevector scaling,surface critical behavior,and wetting in the 2-d, 3-state chiral clock model

The controversial 2-d, 3-state chiral Potts model is studied using transfer matrix finite size scaling. at =0, we find dq _N/dN ^–4/5, whereq is the wavevector, the chiral field, andN the strip width (N=4–10). The result is consistent with den Nijs's crossover exponent =1/6. With surface fields on the infinite free boundaries, exponents associated with bulk magnetizationy _H, surface magnetizationy _H, and surface susceptibility are computed vs. ; results are similar for or to the infinite direction. Preliminary results are given for the bulk specific heat critical amplitudes, to test the universality of amplitude ratios. The interface wetting line is located for 01/4 using simple transfer matrix calculations of surface tensions in the solid-on-solid approximation. Overhangs or bubbles seem relatively unimportant at all temperatures.     

The Peierls instability and superconductivity in quasi-2-d La2-x(Ba,Sr)xCuO4 compounds

The Peierls instability in the quasi-2-d La_2-x(Ba,Sr)_xCuO₄ is reexamined by taking the weak interlayer coupling into account. A two-step Peierls transition theory is developed, the general misunderstandings on the Peierls instability are therefore clarified, and a number of experimental anomalies observed in La₂CuO₄ are well explained. By suggesting an additional change of space group symmetries at the lower transition point, the calculated band structures are also intepreted. The possibility of CDW coexistence with the high-T_c superconductivity, the possible evidence for the 3-d superconductivity of the high-T_c materials are discussed with this theory.     

A-B site-bond correlated percolation for antiferromagnetic Ising model: The Bethe cluster approximation

We study the site-bond percolation problem for clusters of holes and particles with antiferromagnetic order by means of the Bethe cluster approximation. We find that the droplets (i.e.P _B =1?e ^?|K|/2) diverge at the antiferromagnetic critical pointH=0,T=T _c; however forH≠0 they diverge along a percolation line which is different from the Antiferromagnetic Phase Boundary except atT=0.     

Critical Casimir effect in three-dimensional Ising systems: measurements on binary wetting films

The critical Casimir force (CF) is observed in thin wetting films of a binary liquid mixture close to the liquid/vapor coexistence. X-ray reflectivity shows thickness (L) enhancement near the bulk consolute point. The extracted Casimir amplitude Delta(+-)=3+/-1 agrees with the theoretical universal value for the antisymmetric 3D Ising films. The onset of CF in the one-phase region occurs at L/xi approximately 5 regardless of whether the bulk correlation length xi is varied with temperature or composition. The shape of the Casimir scaling function depends monotonically on the dimensionality.     

2D Ising Model for Enantiomer Adsorption on Achiral Surfaces: L- and D-Aspartic Acid on Cu(111)

The 2D Ising model is well-formulated to address problems in adsorption thermodynamics. It is particularly well-suited to describing the adsorption isotherms predicting the surface enantiomeric excess, ees, observed during competitive co-adsorption of enantiomers onto achiral surfaces. Herein, we make the direct one-to-one correspondence between the 2D Ising model Hamiltonian and the Hamiltonian used to describe competitive enantiomer adsorption on achiral surfaces. We then demonstrate that adsorption from racemic mixtures of enantiomers and adsorption of prochiral molecules are directly analogous to the Ising model with no applied magnetic field, i.e., the enantiomeric excess on chiral surfaces can be predicted using Onsager’s solution to the 2D Ising model. The implication is that enantiomeric purity on the surface can be achieved during equilibrium exposure of prochiral compounds or racemic mixtures of enantiomers to achiral surfaces.     

The crossover from 2D to 3D percolation: Theory and numerical simulations

We describe here the crossover between 2D and 3D percolation, which we do on cubic and square lattices. As in all problems of critical phenomena, the quantities of interest can be expressed as power laws of , where and h are the percolation threshold and the thickness of the film, respectively. When these quantities are considered on the scale of the thickness h of the films, the corresponding numerical prefactors are of order one. However, for many problems, the scale of interest is the elementary one. The corresponding expressions contain then prefactors in power of h which we calculate. For instance, we show that the mass distribution n(m) of the clusters is given by a master function of , where h is the thickness of the film and are tabulated 2D and 3D critical exponents. We consider also the size R ²(m) of the clusters as a function of their mass m, for which we provide both scaling laws and numerical data. Therefore, any property corresponding to a given moment of mass and size can be obtained from our results. These results might be useful for describing transport properties, such as electric conductivity, or the mechanical properties of thin films made of disordered materials.Received: 24 October 2002, Published online: 26 August 2003PACS: 68.60.-p Physical properties of thin films, nonelectronic - 73.50.-h Electronic transport phenomena in thin films - 05.50. + q Lattice theory and statistics (Ising, Potts, etc.)     

2D-to-3D percolation crossover of metal-insulator composites

Percolation properties and d.c. conductivity were determined for an L²×h-random resistor network model of metal-insulator composite films. The effects of the thickness h on the percolation threshold and conductivity were studied numerically in the limit of an infinite size of the L²-plane parallel to the film. For thicknesses ranging from h/L=0.01 to h/L=0.24, a crossover between a finite-size regime and a saturation regime was observed at h/L≈0.1. In the finite-size regime (h/L?0.01), the percolation threshold scales as pc(h)−pc3∝h−1/x, the exponent x being compatible with that of the critical exponent of the 3D correlation length, ν₃. The conductivity exponent t appeared to depend linearly on the ratio h/L with a slope νD compatible with 2+ν₂, where ν₂ is the 2D correlation length exponent. In the saturation regime, a scaling correction for the percolation threshold was found with an exponent 1+1/ν₃. In this regime we also observed a logarithmic dependence of the conductivity exponent on h/L.     

Planelike Interfaces in Long-Range Ising Models and Connections with Nonlocal Minimal Surfaces

This paper contains three types of results:

• the construction of ground state solutions for a long-range Ising model whose interfaces stay at a bounded distance from any given hyperplane,
• the construction of nonlocal minimal surfaces which stay at a bounded distance from any given hyperplane,
• the reciprocal approximation of ground states for long-range Ising models and nonlocal minimal surfaces.

In particular, we establish the existence of ground state solutions for long-range Ising models with planelike interfaces, which possess scale invariant properties with respect to the periodicity size of the environment. The range of interaction of the Hamiltonian is not necessarily assumed to be finite and also polynomial tails are taken into account (i.e. particles can interact even if they are very far apart the one from the other). In addition, we provide a rigorous bridge between the theory of long-range Ising models and that of nonlocal minimal surfaces, via some precise limit result.

     

3D short-range wetting and nonlocality

Analysis of a microscopic Landau-Ginzburg-Wilson model of 3D short-ranged wetting shows that correlation functions are characterized by two length scales, not one, as previously thought. This has a simple diagrammatic explanation using a nonlocal interfacial Hamiltonian and yields a thermodynamically consistent theory of wetting in keeping with exact sum rules. For critical wetting the second length serves to lower the cutoff in the spectrum of interfacial fluctuations determining the repulsion from the wall. We show how this corrects previous renormalization group predictions for fluctuation effects, based on local interfacial Hamiltonians. In particular, lowering the cutoff leads to a substantial reduction in the effective value of the wetting parameter and prevents the transition being driven first order. Quantitative comparison with Ising model simulation studies due to Binder, Landau, and co-workers is also made.     

Crystal-Field Effect of spin-3/2 Transverse Ising Model

The crystal-field effect of spin-3/2 transverse Ising model is studied with the scheme of mean-field approximation. The influences of the crystal field and the transverse field on the phase diagram of the system are discussed.     

Ising model in a quasiperiodic transverse field,percolation, and contact processes in quasiperiodic environments

Quantum Ising models in a transverse field are related to continuous-time percolation processes whose oriented percolation versions are contact processes. We study such models in the presence of quasiperiodic disorder and prove localization in the ground state, no percolation, and extinction, respectively, for sufficiently large disorder.