Bulk and surface properties in the critical phase of the two-dimensionalXYmodel

Domain growth and aging in the random field XY model: A Monte Carlo study

We use large-scale Monte Carlo simulations to obtain comprehensive results for domain growth and aging in the random field XY model in dimensions d=2,3. After a deep quench from the paramagnetic phase, the system orders locally via annihilation of topological defects, i.e., vortices and antivortices. The evolution morphology of the system is characterized by the correlation function and the structure factor of the magnetization field. We find that these quantities obey dynamical scaling, and their scaling function is independent of the disorder strength Δ. However, the scaling form of the autocorrelation function is found to be dependent on Δ, i.e., superuniversality is violated. The large-t behavior of the autocorrelation function is explored by studying aging and autocorrelation exponents. We also investigate the characteristic growth law L(t,Δ) in d=2,3, which shows an asymptotic logarithmic behavior: L(t,Δ)∼Δ^{-φ}(lnt)^{1/ψ}, with exponents φ,ψ>0.

Nonequilibrium phase transition in a driven Potts model with friction

We consider magnetic friction between two systems of q-state Potts spins which are moving along their boundaries with a relative constant velocity ν. Due to the interaction between the surface spins there is a permanent energy flow and the system is in a steady state, which is far from equilibrium. The problem is treated analytically in the limit ν=∞ (in one dimension, as well as in two dimensions for large-q values) and for v and q finite by Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase transitions take place, the properties of which depend on the type of phase transition in equilibrium. When this latter transition is of first order, a sequence of second- and first-order nonequilibrium transitions can be observed when the interaction is varied.

Ordering of two-dimensional crystals confined in strips of finite width

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential proportional, variantr;{-12} in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D ) depends very sensitively on the precise boundary conditions at the two "walls" providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-)long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y direction along the walls then crosses over from the logarithmic increase (characteristic for d=2 ) to a linear increase with n (characteristic for d=1 ). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising and XY models is made.

Lack of long-range order in confined two-dimensional model colloidal crystals

We investigate the nature of the ordered phase for a model of colloidal particles confined within a quasi-one-dimensional (Q1D) strip between two parallel boundaries, or walls, separated a distance D in two dimensions (2D). Using Monte Carlo simulations we find that at densities typical of the bulk 2D triangular solid the order in the D1D strip is determined by the nature of the boundaries. While the order is enhanced for a suitably corrugated boundary potential, for a uniformly repulsive smooth boundary potential ordering normal to the walls is enhanced ("layering"), but destroyed parallel to the wall.

Topological transition in a two-dimensional model of liquid crystal

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O2 vector model characterized by nonlinear nearest neighbor spin interaction governed by the fourth Legendre polynomial P4. The system is studied through standard finite-size scaling and conformal rescaling of density profiles of correlation functions. A topological transition between a paramagnetic phase at high temperature and a critical phase at low temperature is observed. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results.