Surface extrapolation length and director structures in confined nematics

We report the results of Monte Carlo simulations of the Lebwohl--Lasher model of nematic liquid crystals confined to cylindrical cavities with homeotropic anchoring. We show that the ratio of the bulk to surface couplings is not in general equal to the corresponding parameter K/W used in elastic theory (where K is the Frank elastic constant in the one constant approximation and W is the surface anchoring strength). By measuring the temperature dependence of K/W (which is equivalent to the surface extrapolation length) we are able to reconcile the results of our simulations as well as others with the predictions of elastic theory. We find that the rate at which we cool the system from the isotropic to nematic phase plays a crucial role in the development of the final director structure, because of a large free energy barrier separating different director structures as well as the temperature dependence of $K/W$. With a suitably fast cooling rate we are able to keep the system out of a metastable planar state and form an escaped radial structure for large enough systems.Comment: 6 pages, 5 figure

Monte Carlo simulations of Rb2MnF4{\rm Rb_2MnF_4}, a classical Heisenberg antiferromagnet in two-dimensions with dipolar interaction

We study the phase diagram of a quasi-two dimensional magnetic system ${\rm Rb_2MnF_4}$ with Monte Carlo simulations of a classical Heisenberg spin Hamiltonian which includes the dipolar interactions between ${\rm Mn}^{2+}$ spins. Our simulations reveal an Ising-like antiferromagnetic phase at low magnetic fields and an XY phase at high magnetic fields. The boundary between Ising and XY phases is analyzed with a recently proposed finite size scaling technique and found to be consistent with a bicritical point at T=0. We discuss the computational techniques used to handle the weak dipolar interaction and the difference between our phase diagram and the experimental results.Comment: 13 pages 18 figure

Cluster Monte Carlo Simulations of the Nematic--Isotropic Transition

We report the results of simulations of the Lebwohl-Lasher model of the nematic-isotropic transition using a new cluster Monte Carlo algorithm. The algorithm is a modification of the Wolff algorithm for spin systems, and greatly reduces critical slowing down. We calculate the free energy in the neighborhood of the transition for systems up to linear size 70. We find a double well structure with a barrier that grows with increasing system size, obeying finite size scaling for systems of size greater than 35. We thus obtain an estimate of the value of the transition temperature in the thermodynamic limit.Comment: 4 figure

O(4)-Invariant Formulation of the Nodal Liquid

We consider the O(4) symmetric point in the phase diagram of an electron system in which there is a transition between d_{x^2 - y^2} density-wave order and d_{x^2 - y^2} superconductivity. If the pseudospin $SU(2)\subset O(4)$ symmetry is disordered by quantum fluctuations, the Nodal Liquid can result. In this context, we (1) construct a pseudospin $\sigma$-model; (2) discuss its topological excitations; (3) point out the possibility of a {\it pseudospin-Peierls} state and (4) propose a phase diagram for the underdoped cuprate superconductors

Randomly dilute Ising model: A nonperturbative approach

The N-vector cubic model relevant, among others, to the physics of the randomly dilute Ising model is analyzed in arbitrary dimension by means of an exact renormalization-group equation. This study provides a unified picture of its critical physics between two and four dimensions. We give the critical exponents for the three-dimensional randomly dilute Ising model which are in good agreement with experimental and numerical data. The relevance of the cubic anisotropy in the O(N) model is also treated.Comment: 4 pages, published versio

Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation

The critical thermodynamics of the two-dimensional N-vector cubic and MN models is studied within the field-theoretical renormalization-group (RG) approach. The beta functions and critical exponents are calculated in the five-loop approximation and the RG series obtained are resummed using the Borel-Leroy transformation combined with the generalized Pad\'e approximant and conformal mapping techniques. For the cubic model, the RG flows for various N are investigated. For N=2 it is found that the continuous line of fixed points running from the XY fixed point to the Ising one is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both beta functions closer to each another. For the cubic model with N\geq 3, the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N>2 is an artifact of the perturbative analysis. For the quenched dilute O(M) models ($MN$ models with N=0) the results are compatible with a stable pure fixed point for M\geq1. For the MN model with M,N\geq2 all the non-perturbative results are reproduced. In addition a new stable fixed point is found for moderate values of M and N.Comment: 26 pages, 3 figure

Phase-transitions induced by easy-plane anisotropy in the classical Heisenberg antiferromagnet on a triangular lattice: a Monte Carlo simulation

We present the results of Monte Carlo simulations for the antiferromagnetic classical XXZ model with easy-plane exchange anisotropy on the triangular lattice, which causes frustration of the spin alignment. The behaviour of this system is similar to that of the antiferromagnetic XY model on the same lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition, associated to vortex-antivortex unbinding, and of an Ising-like one due to the chirality, the latter occurring at a slightly higher temperature. Data for internal energy, specific heat, magnetic susceptibility, correlation length, and some properties associated with the chirality are reported in a broad temperature range, for lattice sizes ranging from 24x24 to 120x120; four values of the easy-plane anisotropy are considered. Moving from the strongest towards the weakest anisotropy (1%) the thermodynamic quantities tend to the isotropic model behaviour, and the two transition temperatures decrease by about 25% and 22%, respectively.Comment: 11 pages, 13 figures (embedded by psfig), 3 table

Long Wavelength Anomalous Diffusion Mode in the 2D XY Dipole Magnet

In 2D XY ferromagnet the dipole force induces a strong interaction between spin-waves in the long-wavelength limit. The major effect of this interaction is the transformation of a propagating spin-wave into a diffusion mode. We study the anomalous dynamics of such diffusion modes. We find that the Janssen-De Dominics functional, which governs this dynamics, approaches the non-Gaussian fixed-point. A spin-wave propagates by an anomalous anisotropic diffusion with the dispersion relation: $i\omega{\sim}k_{y}^{\Delta_y}$ and $i\omega{\sim}k_{x}^{\Delta_x}$, where ${\Delta_y}=47/27$ and ${\Delta_x}=47/36$. The low-frequency response to the external magnetic field is found.Comment: 34 pages, RevTeX, 2 .ps figures, the third figure is available upon reques

Phase-ordering dynamics of the Gay-Berne nematic liquid crystal

Phase-ordering dynamics in nematic liquid crystals has been the subject of much active investigation in recent years in theory, experiments and simulations. With a rapid quench from the isotropic to nematic phase a large number of topological defects are formed and dominate the subsequent equilibration process. We present here the results of a molecular dynamics simulation of the Gay-Berne model of liquid crystals after such a quench in a system with 65536 molecules. Twist disclination lines as well as type-1 lines and monopoles were observed. Evidence of dynamical scaling was found in the behavior of the spatial correlation function and the density of disclination lines. However, the behavior of the structure factor provides a more sensitive measure of scaling, and we observed a crossover from a defect dominated regime at small values of the wavevector to a thermal fluctuation dominated regime at large wavevector.Comment: 18 pages, 16 figures, animations available at http://www.physics.brown.edu/Users/faculty/pelcovits/lc/coarsening.htm

Critical equation of state of randomly dilute Ising systems

We determine the critical equation of state of three-dimensional randomly dilute Ising systems, i.e. of the random-exchange Ising universality class. We first consider the small-magnetization expansion of the Helmholtz free energy in the high-temperature phase. Then, we apply a systematic approximation scheme of the equation of state in the whole critical regime, that is based on polynomial parametric representations matching the small-magnetization of the Helmholtz free energy and satisfying a global stationarity condition. These results allow us to estimate several universal amplitude ratios, such as the ratio A^+/A^- of the specific-heat amplitudes. Our best estimate A^+/A^-=1.6(3) is in good agreement with experimental results on dilute uniaxial antiferromagnets.Comment: 21 pages, 1 figure, refs adde