Interfacial adsorption phenomena of the three-dimensional three-state Potts model

We study the interfacial adsorption phenomena of the three-state ferromagnetic Potts model on the simple cubic lattice by the Monte Carlo method. Finite-size scaling analyses of the net-adsorption yield the evidence of the phase transition being of first-order and $k_{\rm B} T_{\rm C} / J = 1.8166 (2)$.Comment: 14 page

Commensurate and modulated magnetic phases in orthorhombic A1C60

Competing magnetically ordered structures in polymerized orthorhombic A1C60 are studied. A mean-field theory for the equilibrium phases is developed using an Ising model and a classical Heisenberg model to describe the competition between inter- and intra-chain magnetic order in the solid. In the Ising model, the limiting commensurate one-dimensional and three-dimensional phases are separated by a commensurate three-sublattice state and by two sectors containing higher-order commensurate phases. For the Heisenberg model the quasi-1D phase is never the equilibrium state; instead the 3D commensurate phases exhibits a transition to a continuum of coplanar spiral magnetic phases.Comment: 11 pages REVTeX 3.0 plus 4 figures appende

Local scale invariance and strongly anisotropic equilibrium critical systems

A new set of infinitesimal transformations generalizing scale invariance for strongly anisotropic critical systems is considered. It is shown that such a generalization is possible if the anisotropy exponent \theta =2/N, with N=1,2,3 ... Differential equations for the two-point function are derived and explicitly solved for all values of N. Known special cases are conformal invariance (N=2) and Schr\"odinger invariance (N=1). For N=4 and N=6, the results contain as special cases the exactly known scaling forms obtained for the spin-spin correlation function in the axial next nearest neighbor spherical (ANNNS) model at its Lifshitz points of first and second order.Comment: 4 pages Revtex, no figures, with file multicol.sty, to appear in PR

Array-induced collective transport in the Brownian motion of coupled nonlinear oscillator systems

Brownian motion of an array of harmonically coupled particles subject to a periodic substrate potential and driven by an external bias is investigated. In the linear response limit (small bias), the coupling between particles may enhance the diffusion process, depending on the competition between the harmonic chain and the substrate potential. An analytical formula of the diffusion rate for the single-particle case is also obtained. In the nonlinear response regime, the moving kink may become phase-locked to its radiated phonon waves, hence the mobility of the chain may decrease as one increases the external force.Comment: 4 figures, to appear in Phys. Rev.

On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet

We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin correlation functions (from which averaged correlation lengths, $\xi^{ave}$, are computed) by transfer-matrix methods. An {\it ansatz} for the size-dependence of logarithmic corrections to $\xi^{ave}$ is proposed. Data for both random-bond and site-diluted systems show that pure system behaviour (with $\nu=1$) is recovered if these corrections are incorporated, discarding the weak--universality scenario.Comment: RevTeX code, 4 pages plus 2 Postscript figures; to appear in Physical Review B Rapid Communication

A new picture of the Lifshitz critical behavior

New field theoretic renormalization group methods are developed to describe in a unified fashion the critical exponents of an m-fold Lifshitz point at the two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close to 8) situations. The general theory is illustrated for the N-vector phi^4 model describing a d-dimensional system. A new regularization and renormalization procedure is presented for both types of Lifshitz behavior. The anisotropic cases are formulated with two independent renormalization group transformations. The description of the isotropic behavior requires only one type of renormalization group transformation. We point out the conceptual advantages implicit in this picture and show how this framework is related to other previous renormalization group treatments for the Lifshitz problem. The Feynman diagrams of arbitrary loop-order can be performed analytically provided these integrals are considered to be homogeneous functions of the external momenta scales. The anisotropic universality class (N,d,m) reduces easily to the Ising-like (N,d) when m=0. We show that the isotropic universality class (N,m) when m is close to 8 cannot be obtained from the anisotropic one in the limit d --> m near 8. The exponents for the uniaxial case d=3, N=m=1 are in good agreement with recent Monte Carlo simulations for the ANNNI model.Comment: 48 pages, no figures, two typos fixe

Specific heat amplitude ratios for anisotropic Lifshitz critical behaviors

We determine the specific heat amplitude ratio near a $m$-axial Lifshitz point and show its universal character. Using a recent renormalization group picture along with new field-theoretical $\epsilon_{L}$-expansion techniques, we established this amplitude ratio at one-loop order. We estimate the numerical value of this amplitude ratio for $m=1$ and $d=3$. The result is in very good agreement with its experimental measurement on the magnetic material $MnP$. It is shown that in the limit $m \to 0$ it trivially reduces to the Ising-like amplitude ratio.Comment: 8 pages, RevTex, accepted as a Brief Report in Physical Review

Dynamical frustration in ANNNI model and annealing

Zero temperature quench in the Axial Next Nearest Neighbour Ising (ANNNI) model fails to bring it to its ground state for a certain range of values of the frustration parameter $\kappa$, the ratio of the next nearest neighbour antiferromagnetic interaction strength to the nearest neighbour one. We apply several annealing methods, both classical and quantum, and observe that the behaviour of the residual energy and the order parameter depends on the value of $\kappa$ strongly. Classical or thermal annealing is found to be adequate for small values of $\kappa$. However, neither classical nor quantum annealing is effective at values of $\kappa$ close to the fully frustrated point $\kappa=0.5$, where the residual energy shows a very slow algebraic decay with the number of MCS.Comment: 6 pages,10 figures, to be published in Proceedings of " The International Workshop on Quantum annealing and other Optimization Methods

Landau model for uniaxial systems with complex order parameter

We study the Landau model for uniaxial incommensurate-commensurate systems of the I class by keeping Umklapp terms of third and fourth order in the expansion of the free energy. It applies to systems in which the soft mode minimum lies between the corresponding commensurate wave numbers. The minimization of the Landau functional leads to the sine-Gordon equation with two nonlinear terms, equivalent to the equation of motion for the well-known classical mechanical problem of two mixing resonances. We calculate the average free energies for periodic, quasiperiodic and chaotic solutions of this equation, and show that in the regime of finite strengths of Umklapp terms only periodic solutions are absolute minima of the free energy, so that the phase diagram contains only commensurate configurations. The phase transitions between neighboring configurations are of the first order, and the wave number of ordering goes through harmless staircase with a finite number of steps. These results are the basis for the interpretation of phase diagrams for some materials from the I class of incommensurate-commensurate systems, in particular of those for A$_2$BX$_4$ and BCCD compounds. Also, we argue that chaotic barriers which separate metastable periodic solutions represent an intrinsic mechanism for observed memory effects and thermal hystereses.Comment: 12 pages, 14 figures, LaTeX, to be published in Phys. Rev.